The Pelion, Greece

Dramatic mountain scenery, unspoilt sandy beaches, pretty mountain villages – the Pelion is gorgeous and yet untouched by mass tourism. Base yourself at the Lost Unicorn Hotel, in the mountain village of Tsangarada, which the owners have filled with antiques and curios, and which also has a library and good restaurant, and explore the area on foot or, if you prefer the idea of sipping strong coffee in sleepy village squares rather than hiking, by car.
• A seven-night B&B stay in September costs from £789pp (two sharing), including flights from Gatwick and car hire with Sunvil Holidays (020-8758 4758, sunvil.co.uk)

Puglia, Italy

Puglia, Italy's stiletto heel, boasts gorgeously baroque architecture, villages of curious trulli (conical-roofed) houses and olive groves stretching as far as the eye can see. As well as being a magnet for cultural tourists, it's also a top destination for gourmet travellers, thanks to a microclimate that produces many of the world's tastiest ingredients, not to mention seafood from the Adriatic. Then there's the weather – in September it will be pleasantly warm (early 20s) rather than scorching. The 17th-century Palazzo Guiglielmo in the heart of the sleepy town of Vignacastrisi makes a restful base. This grand-looking but quiet B&B has six rooms and plenty of outdoor space – courtyard, pool, rooftop terrace – for you to find a peaceful corner to get stuck into those books you've been meaning to read all summer. If you have a car, it's a short (3km) drive to the seaside which will be pleasantly uncrowded now that the Italian holidaymakers are back to work, and the historic city of Lecce (45km) will make a great day trip. Stay between 5 September and 9 October and get a 20% discount on the accommodation, making a week in September £308pp on a B&B basis, or £635pp with flights and car hire.
• Long Travel, (01694 722193, long-travel.co.uk)

Valletta House, Malta

Malta has a reputation for being a granny-magnet but it's not all blue-rinse tours. This romantic apartment, housed in a 16th-century building in the heart of the capital Valletta, makes a glamorous base for style-conscious lovers, with its stone arches in the kitchen, Maltese limestone and works of art and tapestries on the walls. Potter around sunny Valletta then return to an apartment fit for a knight.
• 07813 988827, vallettahouse.com, from €85 a night, including private airport pick-up (sleeps two, seven-night minimum stay),

Porto Rafael, Sardinia

Romantic bolt holes like this – there are sea views from the terrace and a private pathway down to a small quiet beach – don't come cheap in Sardinia, but for the week starting 10 September the Rosetta studio apartment is available for £350, a saving of £220 (excluding flights). Porto Rafael is a discreet and charming village in the north of the island, opposite the Maddalena islands, a protected marine park accessible by boat. The apartment sits below the main villa but has its own entrance and is just a two-minute minute walk to the square, bar and supermarket – but it's the kind of place where you'll probably want to stay home and dine alfresco overlooking the water.
• Essential Italy (01223 460100, essentialitaly.co.uk, sleeps two)

Inland Portugal

Marvão, Portugal. Photograph: Stefano Amantini/Atlantide/Phototravel/Corbis

Barretos is a picturesque, time-stood-still village of white houses, narrow cobbled streets and Gothic arches in Portugal's sleepy Alentejo region – a fitting location for the peaceful 19th-century Coat of Arms cottage. The stylishly restored three-bedroom property is surrounded by olive groves, cork oak trees and ancient pathways. Late summer is the perfect time to visit the Alentejo, when it is still hot enough to enjoy the cottage's garden, sun terrace and plunge pool, but the temperature has dropped from its sizzling 40C mid-summer high. Nearby is the historic village and castle of Marvão, one of the most beautiful in the region.
• Available from 18 September-1 October through oneoffplaces.co.uk. Usually £520, now £365 for one week (sleeps six)

Lycian coast, Turkey

If you're after pure R&R – no traipsing around the sights, no strenuous exercise – then this could be the deal for you. Villarenters has a 55% discount on a two-bedroom apartment in the fishing village of Gumusluk, on Turkey's Lycian coast, if your departure date is within one week of the booking date. It's part of a complex, overlooking the turquoise sea, with the village on your doorstep should you decide to prise yourself away from the shared pool. In the evening wander down to the village for dinner. Prices start from £235 per week for hire of the villa, reduced to £105 per week after discount based on up to five sharing.
• Book through villarenters.com (property reference: 8968). The nearest airport is Bodrum – fly there with easyJet from Gatwick, Stansted, Bristol or Liverpool

Marrakech, Morocco

Riad Farnatchi, Marrakech

Tourism to Marrakech has still not recovered following the bomb attack in the main square in April, and the knock-on effect of the Arab spring. For tourists that means there are bargains to be had. Throughout September, Black Tomato is offering four nights for the price of three at Riad Farnatchi in the medina, five minutes from the souks and 10 from Djemma al Fna. And although the riad is in the heart of the action, inside it's a sanctuary of modern chic design with large balconies and a gorgeous courtyard pool. A white marble hammam is available for guests and the stylish rooms and suites come with complimentary cream-coloured kaftans and comfy tasselled babouches.
• 0207-426 9888, blacktomato.co.uk.From £520pp B&B including flights (or £400 without flights), plus transfers and dinner on one night

Sailing flotilla, Greece

Can't face going back to work? Then sail off into a Greek sunset … at least for a week. Sunvil Sailing is offering a week's flotilla sailing with optional tuition during September from £600pp, a saving of up to £274pp on the brochure price. You set sail from Lefkas to explore some of the Ionian islands, including Meganissi, Kastos, Kalomos, Cephalonia and Ithaca. Never sailed before? Then use this as an opportunity to learn the ropes with a qualified instructor, while experienced sailors can crew their own yachts in the flotilla. The price is based on two sharing a cabin and includes flights from Gatwick and transfers, but not food (there is an on-board kitty towards food) and the yachts moor up at a different port each evening for dinner ashore.
• 020-8758 4780, sunvilsailing.co.uk

There is a special feeling when you give that final turn of the key in the lock and set off on a house exchange. A faint wondering, alongside the travel excitement, if you are doing something rather unwise. Who are you about to allow into your home? Are they, at this very moment, speeding down the motorway in a removal truck? Will you arrive at your exchange destination to find the door barred? Or to find no house at all? This time my feeling of uncertainty was a little stronger, if only because our destination was less settled than any we had visited before. We were going to Morocco.

We live in Rome, a city we love, but love rather less in July and August. By late June we find ourselves dreaming of cooler, greener places. Fortunately Rome appeals to people eager to escape their own cool greenery. Summer exchanges have taken us to Vancouver and the French Alps and Pyrenees. We were first drawn to house swaps simply as a means to travel without breaking the bank, but we soon discovered they had other charms. Though we have only met one of the families we have exchanged with, I have the curious feeling that we know them all. We felt welcome in their homes, learned something of how they ordered their lives, and – following their advice – visited their favourite local spots, shopped at their favourite shops and ate in their favourite restaurants. They did the same, in Rome, and during our stays we kept in regular contact, comparing notes.

This year it began to look doubtful that we would do an exchange. By mid-April nothing promising had come up – until a French family wrote, offering their holiday home in Essaouira, on the Atlantic coast of Morocco. The pictures looked beautiful, and included in the swap was a cleaner-cook who, if we gave her some money to buy food at the market, would make us breakfast and dinner: unheard-of luxury for a house exchange. Our children had never been south of Europe, and though I was doubtful about the heat, Morocco would be an exciting new experience for them. For that matter it could be an exciting experience for their parents: to get a glimpse of the Arab spring at first hand.

The prospect seemed less enticing soon after we agreed the swap, when we learned of the horrors of the Marrakech café bomb. I suspect the chief peril of house swapping is not vandalism or robbery, but that your exchangers will suddenly change their minds, leaving you with a fistful of air tickets and nowhere to go. In this case, though, we never thought seriously of cancelling. The bomb seemed an isolated event.

Luckily this proved to be the case. Arriving in Marrakech, the greatest dangers seemed to be the 45 degree heat, the motorbikes roaring through the maze-like alleyways of the souk and the "guides" who would lead you in endless circles around the old town to earn a good tip. The city, though a visual feast, was a place where affluent foreigners met poor locals head on, and it showed. The first casualty – at least for the westerners – was reliable information. All facts, from the price of a pair of slippers to the best way to get to the coast, were complicated by hopes of money. Fortunately, even in Marrakech, 100 miles from our house-swap destination, we were helped by our exchange, who had given us the number of a contact in Essaouira, Hamsa. When we rang him he quickly arranged a comfortable car at a fair price.

Safe landing: the tall and narrow house was "even more beautiful than in the photos".

So we reached our new home. The house was beautiful – even more so than in the photos on the exchange website – and intriguingly tall and narrow, like an upturned matchbox. Stairs rose vertiginously to a small roof terrace from where you could see Atlantic breakers crashing on to the rocky shore. The house was also a little damp, but this, as we quickly realised, was a hazard of Essaouira. The town is renowned as a windsurfers' paradise. As such it is buffeted by fierce winds, which become decidedly chilly by evening, and we found ourselves short of warm clothes. The sea, too, was cold, and all in all it felt a little like Cornwall with camels. At least we didn't have to worry about searing heat. In all other respects, though, Essaouira proved an excellent destination. It allowed our children, who had been rather discouraged by the hassle of Marrakech, to discover a gentler Morocco. Our cleaner-cook, Hayat, was warm and friendly, as were most people we met in the town. I was struck by a sense of old-fashioned neighbourliness; café bombs seemed very far away here.

Another surprise was the variety of lifestyles. As we sat on Essaouira's beach in the bracing wind, I was surprised by how the Moroccan women around us had every kind of appearance, from burqas (fairly rare) to head scarves and flowing gowns, and bare heads and bikinis. What was more, one group might include a complete mix of styles. Though the women mostly kept out of the water (and who could blame them?), leaving the waves to the men, a few waded into the surf in their flowing dresses. There was about the whole scene, I realised, something Victorian.

Matthew's wife and children in the Atlantic.

We met our swappers' contact, Hamsa, and he showed us where to find the town's best coffee and where to eat well. Moroccan food was another great discovery of the visit. It is surely one of the world's great cuisines, and when not enjoying Hayat's fine home cooking, we tried delicious tajines and couscous in local restaurants and ate freshly caught crab and sardines at cafés by the port.

So we got to know our temporary home. My wife Shannon took our seven-year-old daughter to a hamam, from where she returned triumphantly recounting how she had been mud-splattered, scraped and scented and then painted with elaborate henna swirls. In the little souk we spent time in the fish market and looking at fossils and magic boxes. Our son was particularly delighted when a spice stall owner let him hold its resident chameleon (a shrewd sales technique).

All the while Morocco was undergoing a quiet revolution. We had seen it when driving from Marrakech to Essaouira. It was Friday – the traditional protest day – and we saw a good number of demonstrations: processions of cars passing very slowly through dusty towns, passengers holding up huge red-and-green Moroccan flags. In Essaouira everyone we met was eager to talk politics. Their views seemed broadly the same: they were disgusted by the corruption of the country's long-entrenched administration but still had a wary faith in the king, Mohamed VI.

Corruption was visible most of all through what you could not see. It was impossible not to be struck by the scarcity of computers. Though Essaouira had two internet cafés, they barely functioned, as the telephone lines were so poor. In an information age, Morocco had been left by the wayside.

Yet change was coming. The day after the protests a referendum was held on reforms to limit the king's near-absolutist powers. We could see the result – a 98% majority for reform – in the smiles of the people on Essaouira's streets. It was exciting to find ourselves witnesses to this moment of hope.

I need not have worried as I turned the key in the lock to leave our Rome apartment. Our swappers had enjoyed Rome, and we found everything just as it had been.

Essentials

Homeexchange.com, which the Kneales used for their house swap, offers 40,000 listings in 143 countries, with membership schemes from £6 a month. The Guardian's house swap service costs £35 a year; for details visit guardianhome exchange.co.uk