Cuba is the most exciting island in the Caribbean. Unfortunately, getting there has always been a bit of a drag. The sole scheduled carrier, Cubana (020 7536 8177, www.cubana.cu), stops in the provincial Cuban city of Holguin on the way, making the outward trip a 12-hour schlep — and your only other option has been to go charter.

Now there’s another way. From June 27, Virgin Atlantic (0870 574 7747, www.virgin-atlantic.com) starts the only nonstop scheduled flights from Gatwick to Havana. They will leave twice weekly, with fares starting at £599, and the journey time will be just 9 hours 40 minutes.

Why Cuba? As much for its unique blend of politics, culture and sensuality — Fidel and Che, revolutionary posters and Spanish colonial architecture, salsa and cigars — as for the Caribbean staples of sunshine and beaches. Most visitors, especially first-timers, like to combine the two sides of the island’s character: a few days in the capital, drinking mojitos, listening to salsa and admiring the architecture, followed by a couple of days chilling by the sea, drinking more mojitos.

Not everything in the garden is rosy. The US trade embargo continues to bite, and a Soviet-style bureaucracy makes life hard for local entrepreneurs. Patience is a virtue here. Away from Havana and holiday strips such as Varadero and Trinidad, the tourist infrastructure is creaky: there’s nothing to buy, and the few restaurants that exist are pretty poor. The much-touted paladares (independent family restaurants) are generally good, but it’s pointless recommending any, as they tend to be closed down by envious government officials if they are seen to be doing too well: asking locals is your best bet.

Yet the island’s virtues outweigh all that. The countryside is stunning; the trend for boutique hotels means there’s finally somewhere appealing to stay; the people are charming and friendly; and the weather is hot. It might have a long way to go, but Cuba is on the up.

In Havana, the Museum of the Revolution (Refugio 1; 00 53-5 862 4091, £2.10) is unmissable. Outside is a collection of tanks, military aircraft, and even an armoured tractor; inside is a detailed and fascinating account of the 1959 revolution, the blood and the passion.

The cigar tour at the Partagas factory (Industria 520; 7 862 4604, £5.50), directly behind the Capitolio, is a treat. From the heady scent of tobacco to the shiny skin of the rezagadoras (leaf-graders), the torcedores (rollers) and finally the escogedores (colour-graders), it’s a sensual delight. There’s a good shop on the ground floor, too.

Incidentally, don’t buy cigars from anywhere other than a shop, no matter how authentic they look. They might be fakes, and the real deal is so cheap to start with, it’s not worth taking the risk.

Havana’s old town is sumptuous and just strolling around is a treat in itself, but it’s not the only architectural highlight. The Cuban government is also proud of Trinidad, a picturesque 19th-century sugar town — so much so that it named its most prestigious and expensive brand of cigar after it. Among the remains are a watchtower, 144ft high — from which the notorious slaver Pedro Iznaga could keep an eye on his “employees” toiling in the fields — and relics of the steam railroad used to transport the sugar harvest.

Varadero is not the holiday capital for nothing. The peninsula’s star attraction is 13 miles of fine white sand, raked and cleaned daily. Expect every conceivable watersport, and no hassle.

If you’re in Havana and want a day on the beach, take a cab to the Playas del Este (eastern beaches). For food, try Playa Santa Maria; for deep-sea fishing and peace and quiet, go for Playa Tarara. The 13-mile journey costs £20 each way.

Twenty minutes from downtown Havana, in Miramar, near the Hemingway Marina, is the exclusive Havana Club. There’s no charge to get in, and it has tennis courts, watersports and gourmet restaurants.

The best address in Havana is the Parque Central (7 860 6627), right in the thick of it on the edge of the old town, La Habana Vieja. It might be low on Cuban character, but it’s slick, the air conditioning works and the food is okay. Doubles start at £140.