Many, many students choose to live off-campus. Florida State University is centrally located in Tallahassee, so traveling to and from campus shouldn't be too much of a problem. Over the past few years, at least 20 new apartment complexes have gone up on the outskirts of campus. These newer developments offer amenities such as computer labs, athletic facilities, and gated security. The closer you are to campus, the older and dingier the apartments. Living off-campus can be cheaper than living in a residence hall and can offer you more privacy.
One thing to keep in mind is the City of Tallahassee's Party Patrol. This is a police unit that patrols the residential neighborhoods and responds to party/noise complaints. They are serious about preventing underage drinking and keeping the local residents happy. This doesn't mean you can't enjoy yourself in off-campus housing. You just have to respect your neighbors. Another policy that the Tallahassee City Commission is trying to pass is limiting the number of non-family members living together in a single residence. Since this policy has met with resistance, no action has been taken yet. It is still something to consider, though, if you plan on living off-campus.