Hi, for fly fishing the best area is Playa Larga, about 2 hours south of Havana. There are other great places but they are even further away, in the eastern parts of the island, such as the town of Brasil, or Jucaro.
In Havana, as far as I know there is no fly fishing area. It would be possible to charter a boat in the Marina Hemingway and fish near Havana. It’s expensive and this is mostly for deep sea Marlins. There is a fishing competition held every year at the Marina. There is a tiny bit of info here: http://autenticacuba.com/water-adventures/fishing/#axzz43mZec0zO
As far as I know, fishing from the Marina is not a thing which is actively done and promoted. The government is working on developing this as a line of tourism, but it is not there yet.
Most fishermen will go to Playa Larga, which is beside the Cienaga de Zapata swamp. There is an outfitter with boats that can be chartered. You can also fish without a boat. It’s all set up for fishing and the packages are sold by hotels and tour operators. But you can basically just show up and start fishing if you want.
A taxi from Havana to Playa Larga is about 95$… sometime a bit less. If you are interested I can call some drivers and find you the best price.
Here are some link with some other discussions on the subject:
https://www.lonelyplanet.com/thorntree/forums/americas-cuba/cuba/havana-fly-fishing-day-trip
http://www.flyanglersonline.com/articles/canada/2011/canada20110110.php
https://www.tripadvisor.ca/ShowUserReviews-g147271-d148142-r236390163-Ernest_Hemingway_Marina-Havana_Cuba.html
http://www.descubrircuba.com/index.php?page=en/fishing/cuba-fishing-guide/fishing-details/marina-hemingway
