Were he still alive, Frank Sinatra would now be 90. In his greatest days, the saying was: "It's Frank's world; we just live in it."

That world has to include Cuba. Before the revolution of 1959, which brought down the Batista regime and installed Fidel Castro (still here and 80 this week - though his recent surgery means his birthday party has been postponed until December), Sinatra spent his honeymoon there - with Ava Gardner in 1951.

Sinatra had begun visiting Cuba in 1946, as a guest of mobsters such as Charlie "Lucky" Luciano, living in exile, and New York's Fischetti brothers. My own motivation was a little more vanilla: simply to be back in Frank's world. You could never manage that in Beverly Hills, Las Vegas, Chicago or New York (New York) - the rest of his domain. High bar prices and the Sinatra family estate keep you at arm's length. But in Cuba I hoped that plenty would be both accessible and affordable.

Both departure and arrival gave grounds for encouragement. In the Virgin Clubhouse at Gatwick I had a shoeshine seated underneath black and white framed prints of screen icons such as Audrey Hepburn. "Sinatra's people," I thought. Havana's Aeropuerto Internacional José Martí is today more Soviet than swing - Cuba's infrastructure was funded through Castro's alliance with the old eastern bloc, then the likes of China - still, its PA system was playing Sinatra's "Fly Me To The Moon" when we arrived. A good start.

There was plenty to suggest Sinatra on the journey into town. As I travelled towards Havana centro, passing murals and graffiti acclaiming Castro and Che Guevara, we shared the road with vintage Chevrolets and the odd Model T and Dodge - cars that predate Castro rule. At my hotel, I sunk further into Sinatra nostalgia - the Hotel Nacional de Cuba is where, behind a gothic façade similar to Manhattan's Dakota building, he and Gardner honeymooned.

The lobby still boasts some magnificent original mahogany fixtures and, although the ceilings are part reproduction, they still reflect the splendour of Sinatra's day. The main silver service restaurant, Aguiar, offers the likes of cerdo al mango to keep red-blooded males happy, and quality wine - Antinori's Tignanello - from Ol' Blue Eyes' native Italy.

Sinatra and Gardner stayed in Room 225. Granted a peek, I walked across what's still the original floor. Rooms 211 to 213 were favoured by the mob (and, while I was at the Nacional, occupied by Russians). But for me, just looking out through the window on to a sea-view terrace where Frank and Ava took cocktails at dusk was enrolment into the Rat Pack.

Anything beyond the Nacional was going to be a bonus. The next day I strolled up past the nearby Capri Hotel then took a left turn to the old Havana Hilton. The Capri, currently being refurbished, was an alternative to the Nacional for the Mob. The Havana Hilton, appropriated by revolutionary forces in 1959, is now the Havana Libre. In the lobby, a striking retro glass dome sits over the hotel's central water feature next to the original sweeping staircase. All four ground-floor bars stocked Sinatra's favoured Cutty Sark Scotch. Even at the epicentre of the revolution his watering holes have endured.

It was now time for cocktails. So I took a taxi downtown to La Habana Vieja. El Floridita's Vegas-style strobe signage beckoned. This bar, favoured by Sinatra during his forays beyond the Nacional, remains the "cradle of the daiquiri". I parked myself at the long bar and nursed a cocktail while fighting the temptation to mumble single-stool anthems such as "In The Wee Small Hours". Anyway, El Floridita had booked a local band, wildly received and more than capable of drowning me out. Photographs on the walls from pre revolutionary days suggested that the adjoining restaurant - with a striking red and gold interior that could have come from New York's Chinatown - had lost nothing over the years.

The only problem was the company. And not just tourists taking snaps with mobile phones (Sinatra always had problems with photography). Ernest Hemingway had joined us.

The locals still call him "Papa". Indeed, with a bust, portrait and photograph, El Floridita salutes the man who from 1939 kept a house at San Francisco de Paula, a short drive from Havana.

The next day Hemingway proved unavoidable. In the evening, I went to La Bodeguita del Medio bar and restaurant. The place proudly quotes him: "Daiquiri in El Floridita, mojitos in La Bodeguita del Medio". A visit to Hotel Ambos Mundos, towards the docks - a rooftop bar provides bird's-nest views of the working port - was the same. Likewise, the city cigar houses. Hemingway was everywhere.

The following night, back at La Bodeguita del Medio I enjoyed swordfish with black bean rice, a Cuban tradition. Photographs of Matt Dillon, Ted Turner, Diego Maradona - the biggest frame - and others hang on the walls as proof of their visits. Inevitably, Hemingway's regular attendance is recorded. Sinatra was notably absent.

Thank goodness for Harry Belafonte. I stared up at his portrait amid the more contemporary stars. Then I realised. I was looking instead of listening. All night, La Bodeguita del Medio had throbbed to Cuban sounds. Sinatra loved visiting because music is fundamental to Havana life.

For the next two days, my ears as well as my eyes were open. Everywhere I registered locals hanging out on their porches listening to music. Cars equipped with sound systems in better shape than their engines pumped out rhythms for the pleasure of those hitching a ride home to avoid Havana's creaking transport system.

On my last night, I went to the top of the Edificio Bacardí. This is an art deco legacy of the pre-Castro age. A small consideration to the lift operator enables you to access the very top, up some epic marble staircases. The views are a dramatic reminder of Old Havana.

Today Sinatra would find Havana tougher territory to hang out in. The city's police now number, reputedly, 10,000 and he was never a great fan of law enforcement. Poverty, evident from the queues for basic supplies, would also have affronted him. He never forgot his own family's modest beginnings as immigrants in the US.

Still, there is plenty he would find familiar. Cash, which he always favoured, is king as credit cards incur a hefty 10 per cent surcharge. Hemlines are high and newspapers are scarce. Even if he does have to share it with Hemingway, Cuba - for the time being at least - is still part of Frank's world.