There is so much to do in Havana!
-tour a cigar factory
-take a day trip to La Playa (the beach)
-tour the 4 plazas
-Museo Nacional de Bellas Artes
-Museo de la Revolucion
-classic car ride down the Malecón
USA citizens staying in Cuba have to declare a reason on their passport, and the most frequent is "Support for the Cuban People". How does this relate to lodging? Well - stay at a Casa Particular owned by a Cuban and you are directly supporting Cuban people!
Casa Particulars are even listed on Airbnb now, making them extremely easy to find and use. You can also get local recommendations.
Arriving to Cuba from the USA, you must fly into Havana currently (this could change). You have to have a visa, which you can get from the airline at your departing airport or upon arrival to Havana (but it will cost more).
Once in Havana, cars are very scarce and oil is limited commodity. Renting a car is rare, so most likely rent taxis or a driver.