There's the Lake City range. About 45 minutes north of the University of Florida. It has a 200 yard range, and two 50 yard ranges. It's free and there's no real drawback to it if you can make it IMHO.
There's the Gainesville Target Range. It's quite a bit closer to UF, but they charge an arm and a leg to join, plus it only has 100 and 25 yard ranges.
There's the Fort White Gun Club range. Again, you have to be a member, but membership is more reasonable and they are CMP affiliated so you can get that Danish Garand you've always wanted.
Gainesville Skeet and Trap charges reasonable fees for skeet and trap, but obviously they have no facilities for rifle or handgun.
There's Harry Beckwith's place down near Micanopy. $6 for a half-hour of range time (pretty steep IMHO), but there are bowling pin shoots that are fun.
There's some informal places down in Ocala, but from what I understand, these are mostly gravel pits.
The Lake City range is probably the best of these.