Havana used to be a bit of a headache for travellers. Of course, you wanted to go there — it’s one of the most exciting, life-affirming cities in the western hemisphere. But when you did, there was nowhere decent to stay, and the food was, frankly, terrible.

What a difference five years makes. Back then, there was a solitary boutique hotel in La Habana Vieja — Hostal Valencia — and virtually nowhere to get a decent meal. Today, there are almost 20 small hotels and scores of new restaurants. Old Havana is being gentrified — and without any loss of innocence or authenticity. The fabric of the place survives.

The new hotels are all fashioned from former mansions — you can see similar refurbishments underway across town. In contrast to other parts of Cuba, such as the infamous Varadero beach strip, the worst sins of mass tourism — monstrous high-rise hotels, low-quality international cuisine — have been avoided. Instead, the old town has been rejuvenated: its pretty Spanish squares cleaned up and floodlit at night, its cobblestoned roads closed to traffic by rows of ancient cannons.

For those who would prefer their Havana with the rough edges left on, thank you very much, there is always Centro Habana. Next to the old town, it is every bit as architecturally stimulating and evocative, but remains, reassuringly, just that little bit shabby.

Feel the pulse: the cheapest and best way to get a taste of this beautiful and anarchic city is at a plastic table outside the 24-hour Capitolio Bar, at Parque Central. It’s on the fault line between La Habana Vieja and Centro, and thrums with life.

A dollar buys a Cuban Cristal beer and a front-row seat to view all that is balmy, sexy, seductive and bizarre about this faded beauty. Expect a parade of vintage US cars, paunchy men in panama hats, with pencil moustaches, waves of Lycra and flashing smiles.

Museums: little museums are springing up all over La Habana Vieja. They’re a cheap diversion, but you’re better off concentrating on the big stuff, notably the Museum of the Revolution inside the former presidential palace (Refugio 1; £2.75; 9am-4.45pm, closed Sunday). You can’t miss it — outside, there’s a collection of tanks, military aircraft and even an armoured tractor. Inside, there is a fascinating account of the 1959 revolution. Some of the rhetoric is comically clichéd, but the blood and the passion is all there.

The other must-see is the Museo Nacional de Bellas Artes (Calle Trocadero; £3; Tuesday-Saturday 10am-6pm, Sunday 10am-2pm) — recently renovated and offering a marvellous glimpse of colonial Cuba, plus works by notable European painters such as Goya and Velázquez.

Vedado: the architectural flip side of Havana — very different from the rich colonialism of Old Havana — is the Vedado, a kilometre to the west of the Capitolio. This is a sort of Miami South Beach writ large (minus the pastel paintwork), an art-deco district of stunning villas, hotels and casinos.

From the former Hilton hotel, renamed Habana Libre after the revolution, drop south along Avenida de la Universidad to the Soviet-style Plaza de la Revolucion. Its centrepiece is a statue of José Martí, the poet and essayist who did much to shape Cuban independence. On the north side of the plaza is a vast mural of that most charismatic of revolutionaries, and T-shirt icon, Che Guevara.

Shopping: Havana has lots of good local art. I paid £13 for a small, two-colour block print at Israel Gonzalez Rivero’s studio (Obispo 255); larger, framed paintings go for 10 times that. Back towards the Capitolio, Galeria Manos (Obispo 411) is an artisans’ co-operative, with splendid handmade crafts, from pottery to humidors, jewellery to papier-mâché dolls.

You’ll be forever coming across traditional Cuban shirts (guayaberas) — four-pocket, short-sleeve jobs from £5-£7.50. They’re cheap and look good, but if you prefer cotton to nylon, try El Quitrin, a couple of doors along from the tourist information office. This delightful rococo boutique has handmade linen clothes for both men and women, from £20.

There is a colourful daily trinket market in front of the Castillo de la Real Fuerza, overlooking the harbour; and if your Spanish is up to it, there’s a fascinating book market on Plaza de Armas.