Strada Santa Cristina, Gubbio, Italy, €9.95m

https://www.italy-sothebysrealty.com/en/for-sale/residential/gubbio-villa_-private-house-2895.aspx

Where The property is at the top of Monte Folone in the Umbrian hills near Gubbio. Perugia airport is 40 minutes by car.

What A recently renovated villa built in 1910 in the Art Nouveau style with 10 bedrooms and 10 bathrooms. There are 10 hectares of land, including a tennis court.

Why The property has two pools on two levels. The upper pool has a glass side and sun terraces, while the lower pool is partially inside and has lanes for lap swimming.

Who Italy Sotheby’s International Realty, tel +39 06 7925 8888

Gaia, Milos, Cyclades, Greece, €5.5m

https://sothebysrealty.gr/properties/gaia/

Where On the south coast of Milos. The island is accessible by boat or plane via a small airport with flights to Athens.

What A modern house designed by Greek architect Christos Vlachos. There are seven bedrooms, all with en-suite bathrooms and terraces with sea views.

Why There are two pools outside with a lounge area between. For sea swimmers, the nearest beach is less than 5km away.

Who Greece Sotheby’s International Realty, tel +30 210 968 1070

Little Hill, Hanover, Jamaica, $6.5m

https://www.christiesrealestate.com/eng/sales/detail/170-l-141-1803301018549974/little-hill-hanover-jm

Where At the top of a small hill in the Tryall Club resort, on the north-west tip of the island. Sangster International airport is about an hour’s drive.

What A 10,000 sq ft villa built in 1959 in a classic West Indian style. Outdoors is a 100ft-long covered terrace with seating for 24. There are also staff quarters.

Why The doughnut-shaped villa is built around a circular swimming pool, 30ft in diameter. The Caribbean Sea is a short drive.

Who Christie’s International Real Estate, tel +1 561 805 7327

Bathwick Hill House, Bath, UK, £4.5m

https://www.carterjonas.co.uk/house/for-sale/bath/bth180240

Where On a hill overlooking the Unesco World Heritage-designated city of Bath. The city centre is within walking distance. Bristol airport is an hour’s drive.

What A five-bedroom, Grade II-listed Georgian villa on 1.7 acres. A separate lodge house has a further two bedrooms and could be used for extra income.

Why The original Italianate garden building has been remodelled to form a pool house with sliding glass doors, frescoes and Doric columns. Bath itself has natural thermal baths.

Who Carter Jonas, tel +44 1225 562 614

1 Potato Island, Branford, Connecticut, US, $4.9m

https://www.christiesrealestate.com/eng/sales/detail/170-l-78183-1805101311556549/1-potato-island-branford-ct-06405

Where The property is the only house on Potato Island, part of the Thimble Islands archipelago in Long Island Sound. The nearest large airport is JFK in New York City, about 85 miles away.

What The main house was built in 1912 and is on the south side of the island. A wraparound porch has views of the landscaped gardens, surrounding islands and the sea.

Why As well as swimming available straight off the dock, there is a heated pool in the centre of the island, plus a hot tub nestled into the rocks.

Who Christie’s International Real Estate, tel +1 203 245 1593

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