The beaches to the East of Havana are only a 20-minute 15-pesos cabride away and they are excellent. Unlike Varadero, there is no resort-atmosphere and the separation between tourist and local doesn't exist.
The water is extremely clear and perfect for swimming
The Playas de Este are a string of beaches just outside of Habana city. They are absolutely beautiful, and well-worth the trip. Any taxi will take you out there for about $20, however you can also take the bus out there, which is much cheaper. Bus # 400 from the train station will take you directly there for a few pesos, although it will get extremely crowded. If you take the bus you should also make sure to ask someone on the bus which stop to get off at for the beach (the beach we went to mostly was Santa Maria del Mar). From there it is about a 15 minute walk to the coast, but well worth the trip! On the way back you can catch the bus along the side of the road, and shouldn't have to wait more than 1/2 hour. There are also taxis going back.