Cuba is a truly beautiful place that more Americans should experience, especially before the island changes dramatically due to increased openness and development.
Don't let the recent rollback dissuade you; licensed groups can still travel to the island on commercial flights and Cuba is an amazing place that is well worth the hurdles.
For first time visitors, I would recommend a few places to see:
The capital of Cuba is also by far its largest and most open city. Visitors will be captured by its beautiful charm, particularly the old and colonial sections as well as the miles-long Malencon on the oceanfront. It also remains relatively inexpensive - though that is changing; a nice rent apartment in the city center is now about $50/night and a meal at one of the city's best restaurants runs $10-20 per person. Personally, two food spots that I would recommend are Nazdarovie, a Russian "Soviet" restaurant on the Malencon with amazing ocean views, and Café Archangel, which has the best breakfast in the city. From a cultural standpoint, there are many attractions but the city's main art museum is second to none, and has a world-class collection.
2) Santa Clara
Santa Clara is a sleepy provincial capital and a personal favorite. The city is centered on a town square, which doubles as the main wifi center but its appeal lies in its relaxed charm. It is most famous for its Revolutionary Monument and, after you visit it, I would recommend stopping by the Revolution Museo and Café for one of the better espressos on the island (or try one of their excellent ice cream concoctions). For queer folks, Santa Clara also has El Mejunje, which is one of the largest "welcoming all" venues on the island, and a far nicer place than the Havana gay bars.
Cuba is a Caribbean island, so any article without mentioning beaches would be an injustice. Visitors to Cuba should experience more than the beach - for those just looking for sun, there are many better options - but this area has some nice resorts and is a great place to kick back and relax for a few days of your trip.