Can you name Britain's first seaside resort? Congratulations to those who said Scarborough. Established as a spa town in the 1620s with the discovery of a mineral spring, the resort took its next step a few decades later when a local physician, Dr Wittie, recommended the benefits of a bracing dip in the sea. By the 19th century, Scarborough was the queen of British resorts, rivalled only by Brighton. Victorians flocked to its imposing spa complex (still there) and fine beaches, while three million came each year into the 1950s. The rise of foreign travel in the 1960s, however, hit Scarborough in the same way it did other UK seaside destinations.

The town's renaissance is driven not only by a renewed appreciation of the British seaside but also by new money from northern financial centres such as Leeds, along with an influx of creative types. Its appeal is clear enough. Wide, sandy beaches curve around the town's two bays - the smarter South Bay, with its backdrop of shops, restaurants and hotels, and the North Bay's more bucket-and-spade appeal. A headland divides the two, topped by a 12th-century castle that overlooks a tiny harbour.

Scarborough has culture, too. Not many seaside towns have four theatres, including the acclaimed Stephen Joseph Theatre, where Alan Ayckbourn has premiered most of his 60-odd plays. You can add a well-regarded jazz festival and Britain's last seaside orchestra. Anne Brontë loved the town and used it in Agnes Grey and The Tenant of Wildfell Hall. I look down on the bay from the balcony of the Crown Hotel, whose Victorian elegance is typical of the town's finest buildings. The nearby Grand Hotel is being restored, while Scarborough has its first boutique hotel: Beiderbecke's.

On The Crescent, a line of Grade II listed Georgian houses arc around communal gardens towards the town's 1840s art gallery. I am here, though, to look at Woodend, the former holiday home of the Sitwell family. The house has been sensitively divided by the sculptor Andrew Clay, who is developing a studio complex for the growing community of artists and media professionals (woodendcreative.co.uk). It is due to be unveiled in May - a month in which the Rotunda Museum, a geological museum, will also re-open. Adrian Riley, a web designer, is typical of the town's new creatives. “Scarborough is a perfect blend: big enough for what you need, great train connections, by the sea,” he says. “Friends say I'm living the dream.”

Older residents recall that the town once produced one of the finest dairy ice-creams in the region: Riley's Ice Cream, made by Riley's Dairies, of Hull, Bridlington and Scarborough. Sadly the dairy is no more (its cream pots buried under the pitch of Scarborough Football Club), but the local food scene is evolving to match lifestyle expectations. Carved out of a Georgian house on York Place, Pepper's has notched up a Michelin recommendation, and an Edwardian hairdresser on South Street has been transformed into the gorgeous Francis Tea Room. By the Victorian market building, Café Heart offers a slice of continental cool. “In the two years since we opened, this town has changed so much,” says its owner, Rex Rixon, who swapped work on fashion interiors for the likes of Yves St Laurent to move here. His wife, Lisa, runs a memorabilia store, The Tin Shop, close by.

For families, there are fine schools, too. Transport is also good, with fast trains to York and Leeds. The North York Moors are easily accessible by road. There is further beauty a few miles along the coast: Robin Hood's Bay is one of the prettiest coastal villages in the country, hugely sought after by second-homers. Jason Brine, though, is a newcomer here to stay, having traded finance work for a FTSE company for running a café in “Old Bay”, a higgledy-piggledy settlement of 17th and 18th-century cottages at the foot of a notoriously steep hill. “I've seen houses change hands in this pub,” says Jason, as we share a pint in the Dolphin. Although only half Old Bay's 200 or so houses are lived in permanently, this is not just a holiday village. “There's a lively community here,” Jason says. “And many weekenders come every weekend.” Weekenders and locals alike are catered for by restaurants such as The Bramblewick, where I tucked into luscious scallops and a fine salad featuring the local Yorkshire feta (renamed “fettle” after an EU ruling).

Farther north, Whitby has long enjoyed the spotlight thanks to its link with Bram Stoker's Dracula. It's an appealing place, and not just for the legions of Goths drawn here. On the southern bank of the Esk, below the ruined abbey, a cluster of cobbled streets make up the old town, while a short climb up the north bank brings you to St Hilda's Terrace, with its Georgian piles built for the ship captains who brought wealth to Whitby in the 17th and 18th centuries. Other pretty streets run off towards the seafront overlooking Whitby Sands, where a pair of whalebones form an arch beside a monument to the town's most famous son, Captain Cook. But for those seeking their own new coastline, North Yorkshire is a lot closer than the South Pacific.

FACTFILE

North Yorkshire's average house price rise of 8.9 per cent in the last quarter of 2007 easily beat the 3.7 per cent for Yorkshire generally, according to the Land Registry.

Prices are higher in South Bay than North Bay. Small flats in Victorian houses in South Bay cost £120,000; two-bed Victorian seafront flats from £190,000. In Olive Mount, South Bay, a three-bed semi is £250,000. In pricier Scalby, on the town's edge, four-bed detached houses cost from £500,000.

In the Old Bay area of Robin Hood's Bay a two-bed cottage recently sold in a day, rising from £250,000 to £350,000. You can pay £180,000 for a rundown one-bed cottage to £400,000 for a three-bed with sea view.

Whitby's period cottages go for £150,000 to £200,000. In the St Hilda's Terrace area, four-bed Georgian houses fetch £500,000.

Times recommends

• Second homes: credit crunch casualty or money-spinner?
• How I built my own sliding house
• Top 10 incentives for house buyers