Let your interests dictate where you stay. If you love history and architecture, pick a hotel in La Habana Vieja or Centro. Just be aware that while hotels in Habana Vieja are charming and colorful, they do not offer all of the amenities that you might in large international chain hotels. Wi-Fi service is generally not available, but almost all hotels offer some kind of paid public Internet option.
The Habaguanex chain hotels are based on unique and interesting concepts. For example, Hotel Los Frailes is in an old mansion and is designed as a sort of cloister, complete with monks in frairs' robes. Conde de Villanueva is designed specifically for cigar lovers, and Hotel Ambos Mundos plays up its association with the American writer Ernest Hemingway. Most of these hotels are recommendable.
If you like to play until the wee hours, Vedado offers a Manhattan atmosphere with plenty of nightlife. If you seek peaceful sea breezes, consider staying in Miramar. If you can't decide, head for the Hotel Saratoga, with its rooftop pool, historic setting, unparalleled service in Cuba—and a stone's throw from the historic sites of La Habana Vieja. The closest resort areas to Havana are the Playas del Este, the best of which is Jibacoa; stay here if you want to be in relative proximity to the capital (about 30 minutes east by car) but want more of a resort experience directly on the beach.
Lodging in private houses is highly recommended but difficult to arrange in advance. Any taxi driver can take you directly to a friend or family member with rooms to rent, but you should check the place out carefully before making a deal. Since laws in Cuba change overnight, the rental of private rooms, now legal, could be illegal by tomorrow. Ask at the airport hotel reservation desk.
Nearly all the government-operated hotels take credit cards as long as they aren't affiliated with U.S. banks or companies. For obvious reasons, private houses do not.