There are many recreational activities available in Cuba as well as some spectator sports.

Cuba's fish population has only recently began to be exploited; many inland lakes and wetlands feature a superb selection of fish.

You also can catch huge fish in the Caribbean Sea around Cuba.  There are several tournaments in Cuba, including one named after Ernest Hemingway.  Most of the fishermen compete to catch the biggest marlin.

You should easily be able to find a bicycle in Cuba if you are interested in riding.  There are also tours from many countries that take foreigners on bike tours around the country.

There are many forested areas in Cuba perfect for hiking.  You probably should not camp out, and there a relatively few good trails.

Hunting in another option.  Many hunting reserves are found in Cuba because many Cubans like to hunt.  Most of the game is some sort of bird, but some foreign animals have been introduced as well.  To hunt, one must obtain a hunting permit.

There are water sports.  Scuba diving and sailing are common and excellent in Cuba.  Cuban coasts have many tropical fish as well as larger animals.  You may also see sunken vessels important in the history of Cuba. 

You will need a permit to go sailing.  There are good sailing areas on all sides of Cuba.  The US-Havana Regatta, a sailing competition, came back in 1994.

Cuban teams have always done extremely well in international sports competitions.  As in the US, baseball is considered the national pastime.  The Cuban baseball system is world class, and American teams attract many Cubans as a result.