Park Av nice place with Diamond and Brunswick tables in Orange Park. Bankshots, Q ball decent places in Southside/Beach area. Riggsy's decent as well. Plenty of smaller rooms as well.
Depending on where you are, there is also a retail store - Billiard Factory - that has some great equipment for play, sort of an academy atmosphere, they host tourneys and exhibitions by pros as well. It's on University, pretty centrally located in Jacksonville.
I teach out of there, and do a free clinic the second Wednesday of every month, usually talk and demo for 30 - 40 minutes then people can play for a bit and I walk around and help with whatever. If you can make it, starts at 6pm, introduce yourself if you come. Once done you can drive about 10 minutes and hit 3 of the rooms listed above for more play/practice. PM me if you want more info.
Scott