I went to UF for undergrad and loved it. A great neighborhood to checkout is the Duckpond near downtown (basically bordered by NE 13th St on the north, NE 9th St on the east, W University Ave on the south and NE 1st St on the west). It's a historic area with lovely Victorian area houses that have been carved up into apartments. There are Duckpond apartment listings on Craigslist, but I always found apartments by driving around there looking for "For Rent" signs. Many students live in the Duckpond, but it doesn't have a party atmosphere like areas closer to campus. It's also within close walking distance to downtown: the Hippodrome, the nice public library (a good place to get away from the university), the farmers' market, restaurants, bars, etc.
If you want to get away to the beach, the ocean is about an hour's drive to the east (St. Augustine/Crescent Beach) and the gulf is about an hour's drive to the west (nice little town called Cedar Key). Newnan's Lake is on the east side of town. It's not recreational like Lake Wauburg or on campus like Lake Alice, but it's a serene place to relax. One poster wrote that it's rural and boring ten minutes out of town. Rural, yes, but I disagree with "boring". There are beautiful drives and nice little towns throughout North Central Florida.
It does get pretty hot in NC Florida, but I survived a few summers with no A/C in my car, so it's manageable. A good way to beat the summer heat is to go tubing in the Itchetucknee River.
@ Chande - I don't think that the cohabitation law is ever enforced, but it is a state law, not just a UF policy: http://www.flsenate.gov/Laws/Statutes/2010/798.02
Florida does have some pretty messed-up laws these days, though, as evidenced by the stand-your-ground law and the tragedy of Treyvon Martin.
Congrats to everyone who is considering Florida for grad school and good luck! Feel free to PM me with any specific questions!