It’s my 13th trip to Cuba,” says the Canadian woman in the seat next to me on the flight to Varadero. “Which hotel are you staying in?”

I have no idea. Our plan is to take a two-hour taxi ride into Havana, be dropped in its ancient centre and knock on some doors to find rooms. It takes my neighbour a few moments to come to terms with this.

“I suppose that’s another way of doing it,” she says, sceptically.

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Canada may for now be Cuba’s biggest source of tourists, but most of them head for Varadero’s beach resorts, where the only Cubans they meet are waiters. They emerge solely on chaperoned day trips to Havana or simply to return to the airport.

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My only concern is that a surge in recently deregulated United States travellers might already have filled all available accommodation. But independent travel for a family of four turns out to be entirely straightforward.

Varadero Airport is small and reason­ably efficient, with fixed taxi prices clearly posted. The traffic is light and the driving both cautious and courteous. Within 20 minutes of being dropped in the heart of Old Havana the family is settled in two rooms behind an old colonial frontage awaiting what turns out to be a vast home-cooked dinner. Instead of simply coming to view one of Cuba’s greatest attractions – Havana’s World Heritage-listed sprawl of Spanish colonial architecture – we are staying in some of it.

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Habana Vieja is a directory of decay – a magnificent 4.5-sq-km maze of peeling paintwork, crumbling stone and brick, and, sometimes, complete collapse. Buildings less than a century old are rare, and many date back to nearer the city’s founding, in 1515. It’s a warren that repays endless wandering, a reference work of ornate Spanish architecture that’s been accidentally preserved by neglect and by the lack of funds for redevelopment. There are churches and castles dating back to the 16th century whose bell towers and battlements may be climbed for views across a sea of terracotta roof tiles or across the narrow harbour to the 18th-century Fortaleza de San Carlos de la Cabaña, one of the largest forts in the Americas.

Vast American vehicles of the 1950s, with the suspensions of a water bed, wallow down the potholed streets. Some are so well maintained they look as though they rolled off the production lines only yesterday, while others have a gently crumpled look as if modelled from plasticine by a clumsy child. Almost all are taxis.

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Cuba can also resemble 1980s China. The main sources of danger are uncovered manholes, broken-up footpaths and discon­certingly low-slung cables. There’s a paral­lel convertible peso for foreigners (CUC) but ordinary pesos for Cubans (CUP), worth 25 times less. The hotels and many restaurants are state-run, with levels of service that might generously be described as imprecise if well-intentioned. Shops sometimes have the external glitz of perestroika-era Russia, and the same almost complete absence of contents.

Roadside billboards feature giant portraits of retired Cuban president Fidel Castro beaming at late Venezuelan strongman Hugo Chávez, who is labelled “our best friend”. But Venezuela’s economy is as dead as the leader largely responsible for its collapse, with the result that the Cuba it once supported is also struggling, its own economy now largely dependent upon tourism.

So hotel rates are high and in convert­ible pesos, but the casas particulares, or private houses, clearly marked with an anchor-like symbol on their doors, are economical. Most have only one or two simple rooms to offer, so any mentioned online or in guidebooks are, of course, full. But there are always many in the same street with rooms to spare and, if they’re full, their proprietors are quick to point you to a neighbouring door.

Indeed, it is possible to become part of a game of pass-the-parcel, in which you’re the parcel and, when the rumba stops, you’re outside your new accommodation. When we want to go east to Viñales, a kind of Guilin for beginners, with pretty pointed peaks emerging from lush landscape, our host in Havana knows someone with rooms there and he can sort out a private taxi that will go door to door. The price is more than the bus, but the same as taking a shared taxi, and far more convenient.

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We then allow ourselves to be passed on again in a private taxi to a casa in Trinidad, a city of picture-perfect rusticity, all one-storey houses and cobbled streets. It ends up perhaps a little more expensive than organising our own taxis or rooms, but it made independent travel effortless.

Either way, Cuba proves one of the most rewarding of all the Caribbean islands, offering the perfect combination of culture and beaches. Little bays of white sand and transparent waters, many occupied only by Cubans, are often a short taxi ride away.

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One hit with the children is a wobbly train ride out of Trinidad up a green valley once dominated by sugar mills, and with substantial plantation houses to visit. The train lumbers out of town, being overtaken by cars, then by bicycles and, eventually, by dragonflies. Butterflies fly through one open side of the wooden carriage and out the other without apparently noticing the train’s existence.

The casas themselves, although battered, are also popular. They usually come with unexpected extras: little rooftop terraces, a giant fig tree supplying fruit straight to the table for breakfast, or a parrot that provides an appealing echo to courtyard conversations.

The Cubans are extraordinarily good-humoured considering that their standards of living plummeted with the fall of Soviet Union and continue to drop. They make visitors very welcome, and the home cooking in the casas, with oversized portions of pork, fish, chicken or lobster, is usually the best in terms of both quality and price.

On August 31, JetBlue Flight 387, the first direct commercial flight from the US in decades, touched down in Santa Clara, making it no longer necessary to travel via Mexico or Canada. Cuba is currently full of Europeans trying to beat the rush of Americans once a forecast 20 round-trip daily flights begin. In the opinion of some locals, however, the planes will be mostly full of Cuban Americans who would have come via other routes anyway, and the increase in visitors will not be great.

Whoever does come, though, this McDonald’s- and Coca-Cola-free bastion of official anti-Americanism, with its giant posters of Uncle Sam receiving a crushing blow to the jaw, isn’t going to change overnight.