For BCAPL leagues, you can find that information, along with the days they play here:
http://www.playcsipool.com/find-a-bcapl-league.html
For a list of NAPA leagues, please look here:
http://www.napaleagues.com/finder.php?location=Florida
For VNEA leagues, please look here:
http://www.vnea.com/find-a-league.aspx
For APA leagues, please look here:
https://poolplayers.com/locator/
You can use the above information to not only find areas to play on leagues in your area, but in the surrounding area as well. For more local spots, I'll defer to anyone who lives in the area.