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.

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.

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.

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.

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.