There is something about a weekend in Bath that brings out one's inner Catherine Morland. With its perfectly proportioned terraces, serenely sloping cobbled streets and elegant crescents chastely embracing gated gardens, it's a city that drips decorum from its very building blocks. The quaint, ladylike pursuits of Jane Austen's heroines are still de rigueur here – taking the waters, perambulating in the parks, a spot of shopping and, of course, the clotted-cream ceremonies of an afternoon tea. If I'd happened upon a place to play a hand of whist or dance a cotillion, I would have donned my finest sprigged muslin and surely done so. Resistance is futile. And why resist? Why not cast off the corset of nasty, pacey modern life and sink into Bath's languorous, idle pleasures? Surely, my dear, it would be almost rude not to.
Whether one agrees with Catherine's wide-eyed assessment of the city in Northanger Abbey – "Oh! Who can ever be tired of Bath?" – or with Anne Elliot's world-weary disinclination to move there in Persuasion – "Oh! When shall I leave you again?" – the city undoubtedly has all of the grace, beauty and restraint of an Austen heroine. Its harmonious blend of Regency and Roman lines is unsullied by modern clutter. The creamy stone – radiant and warm in the golden sunset, chilly and severe under a steely winter sky – shimmers with history and old romance. You don't shuffle or march around Bath's attractions, as you do in so many tourist towns, you stroll, maybe even glide. It's like starring in your own personal period drama.
In fact, it's a curious thing, but Austen, who characterised the city with such memorable wit and vim in her first and final novels, never much cared for Bath. When her mother announced that the family would be relocating there from their beloved Steventon, young Jane apparently swooned from shock. Once recovered, she lived there for five years from 1801, before escaping soon after her father's death to Southampton and, from there, to Chawton in Hampshire where she lived peacefully, away from the follies and fripperies of spa society, for the rest of her life.
If you're keen on such follies and fripperies, though, the full Andrew Davies experience is among the things that Bath does best. You can still take a turn at the Assembly Rooms, once a social hub, bristling with bonnets and bustles, now a fitting home to the Fashion Museum. Tea at the Pump Rooms remains a must, too, though these days there is less sipping of the health-giving waters and more scone-scoffing and tinkling piano. And for the truly dedicated Austenophile, there is a museum dedicated to the writer on Gay Street, where she briefly lodged. Elsewhere, No 1 Royal Crescent – the first of John Wood's 30 identical houses that make up the handsome 500ft sweep – is suspended in time with all of its fixtures, fittings and flowers as though Catherine, having dressed in the pretty bedroom upstairs, has just hopped into the sedan chair parked in the hallway and left for a glittering ball.
For all that, Bath is a 21st-century city. The admirals and aristocrats of old have been replaced by new A-list residents, including Johnny Depp and Nicolas Cage, who was so taken with the city's Olde English film-set quality that he bought three properties, including a £4m flat on The Circus. In 2009, he even turned on the Christmas lights after an elderly neighbour pushed a hopeful note through his door. And for visitors – families, couples and hen parties alike – the city offers an up-to-date take on the restorative Bath break, with its Holy Trinity of shopping, spa-ing and socialising.
The best place for the first of these remains the upmarket Milsom Street – the city's most fashionable thoroughfare as it was in Austen's time, though Molland's teashop is now more likely a Reiss. Talking of teashops, Jamie's Italian has also opened a branch here. Outside, the lettering "Circulating Library and Reading Room" is still etched into the stonework. Inside, the labyrinth of 18th-century reading rooms has been converted into a buzzy new social destination. Industrial kitchen chic, laid-back, tasty food and Jamie Oliver's laddy touch – World's Best Olives! Funky Chips! Awesome Chocolate and Espresso Tart! – rub shoulders with the florid wallpaper of centuries past, half-plastered walls and elegant cornices.
Moving on, if in Austen's time the Pump Rooms was the place to "parade up and down for an hour, looking at everybody and speaking to no one", the 21st-century equivalent is surely the Thermae Bath Spa, a sympathetic glass and stone complex of frankincense-infused steam rooms, personal foot-spas and lazy lagoons. The main attraction, though, is the steaming, open-air rooftop pool from where bathers (rather too many to be truly relaxing on a Sunday morning) can cast an eye over busy weekend Bath, deliciously unseen by those on the streets below. Austen's gossipy ladies would surely have approved.
When these social pursuits become too much, the Royal Crescent Hotel offers a welcome retreat. A picture of restraint with its oh-so-discreet entrance in the middle of the city's most desirable address, it combines country-house charm in the main building – open fires and overstuffed sofas in the drawing room, flounces and roll-top baths in the rooms – with a modern, five-star experience in the coach house and stables at the back. Here you find the Bath House Spa, a candle-lit temple to relaxation with a warm rectangular bath running beneath arched windows, plunge pools, steam room and sauna. On a quiet January weekend, we had it almost to ourselves – bliss.
Next door, The Dower House restaurant, refurbished two years ago, an old-fashioned starch-and-silver hotel dining experience is lifted by zingy decor, an exhaustive cocktail list and a menu offering intriguing, delicious treats from newly installed chef David Campbell, such as wobbly slow-cooked duck eggs, herb rolled lamb coated in a honey and lavender reduction, and salted chocolate tart, with blueberry and Horlicks ice-cream.
The hotel's secret weapon, though, is its secluded garden. Overlooked only by the restaurant, it's a private haven in a city built for public peacocking. The few sights and sounds of the Noughties world that the city allows itself, simply melt away. "Bath is still Bath," wrote Austen in a grumpy letter to a friend from her unwelcome city exile. You could send the same postcard today – but is that really such a bad thing?
Alice Jones stayed at the Royal Crescent Hotel, Bath (01225 823 333 B&B rooms from £195 per night); royalcrescent.co.uk
Bath: boats, museums & fine dining
* Bath has designated 2011 Museum Year, offering a packed programme of events with highlights including Bath in 100 Objects, a huge exhibition spread across the city's institutions and outdoor spaces; plus the venerable visual art hub, the Holburne Museum, comes out from under wraps after a multi-million pound renovation and extension; visitbath.co.uk/museums.
* Tour the Kennet & Avon canal aboard Lady Lena, an electric river launch built in 1890 from mahogany, oak, teak and ash. Take a skippered tour; champagne and picnics can be provided. From £50 per person; ladylena.co.uk.
* Explore the Roman Baths by torchlight. From 1 July to31 August you can join an after-dark guided walking tour of the bath house, lit with flaming torches, and learn about its 2,000-year history; romanbaths.co.uk.
* Lucknam Park is an exquisite Georgian gem: gorgeously subtle décor, Michelin-starred food and picture-perfect country surroundings. The spa, illuminated at night with a dramatic fire running along its length, is more James Bond than Jane Austen, however. Rooms from £315 per room per night; lucknampark.co.uk.
* Bath Priory evokes the atmosphere of a private house party at the same time as being one of the city's top foodie destinations, thanks to the efforts of executive chef Michael Caines. The lunch menu is a reasonable £25.50 for two courses. Classic rooms from £195, thebathpriory.co.uk.