My wife to be and I went in the mid-90's, had a long weekend in Havana and stayed at this place
Welcome - Hotel Nacional de Cuba
We were driven around in a 1955 Buick and the driver had to pump the brakes when he wanted to stop. Enjoyed a candle lit meal on the balcony of a locals home and dined of fresh lobster. Listened to the old guys argue about baseball and play chess. In the evening as the sun went down we drank rum and coke on the sea front with all the other young couples.
I've been to a few countries but Cuba is one of the few I would love to go back to, if I had the money and time I'd ship my 4x4 over and travel around the whole island for 4-6 weeks.
If you are not going for long just stick to Havana and soak up the charm before the its spoiled by over tourism