I lived in Gainesville from 2006 - 2013, from ages 18 - 25. Gainesville is a great place to spend your early 20's, but as I occasionally go back, it still has a lot to offer for those in their mid-late twenties. If you want a watering hole, I would suggest Stubbies & Steins, The Top, and 2nd Street Speakeasy as good places to start. Because of the schools, it is quite diverse; you shouldn't get the "not from 'round hurr" attitude. I imagine that its atmosphere is like all other small college towns big on football.
Gainesville is culturally dense; it has a lot of amenities considering its size. There are a ton of nature parks surrounding the city, some scenic driving roads, a few museums, and a ton of great and affordable restaurants. It is also essentially Florida's mature hippy enclave. It has at least three coffee roasters, a farmer's market just about every day of the week, the cultish Hare Krishna community, LBGT parade, and lots of O stickers. I would call it the best place in Florida to commute by bicycle.
Car culture isn't very strong; the track is isolated on the far north side of town. Few know that it exists aside from "ACRs" (Alachua County Residents, the term for natives and long-term non-students). Families primarily live on the western outskirts of town. Most late twenty-somethings I know are graduate students. Unless you have something lined up, there's not a whole lot of work available, aside from retail, healthcare, & teaching.
There are a ton of places in town to rent, but keep in mind that many properties operate on the August 1st - July 31st lease rotation, simply to align with semester scheduling. However, it will be really easy to find subleases starting in May, since a lot of people graduate with a few months left on their rent. This would be a great opportunity to move to town and find a place that you like once you learn the area.
Rent prices went down a bit starting 6 years ago, since a lot of new rental property construction was completed. It may have gone up by now, but I don't know. The last place I lived, a 1920's 3/1 shotgun house with an amazing front porch, was $725/month.