Scott Lee has it right... Crooked Cue is a good 20 mins closer to Bradenton than Strokers. And both are outstanding pool halls.
Strokers has a bigger menu with a fantastic full service kitchen. The food there really is at least two full letter grades better than what you'd probably expect to be served in a pool hall. If you do make the extra trip to Strokers, I would avoid Thursday nights at all costs. That's APA 8-ball night and the place gets packed to the gills with smokers and all tables are usually occupied. Tuesdays is APA 9-ball night there, and there are usually some rental tables available.
The only real place to play in Bradenton when I used to live in that area was Livingstons in Bradenton (at 4828 14th St W, Bradenton, FL) Do not confuse that Livingstons with the one on Clark Rd. in Sarasota, which is more like a Celebration Station family arcade game center.
The thing is... depending on where you live in the greater Sarasota/Bradenton/Palmetto area, if you live (or are staying) in close proximity to I-75, then you are better off driving north and across the skyway bridge into Pinellas County at interstate speeds to get to Crooked Cue.
There is also a bar in St.Pete called Flamingos Sports Bar, which is frequented by some AZ members. I think that place might be another 10 minutes closer to you, but I've never been there so I can't vouch for the quality of the playing environment or food or such. There are some players there, as I have seen some competent APA teams from out of that establishment at the Cities tournaments. Just don't confuse it with "The Flamingo Resort" in South St. Pete which is a flaming gay bar who might be interested in your "other" stick. LOL!
Good luck
