I graduated USF in '96. Back then the off campus housing area was called "suit case city". It probably still is and it's primarily low income housing. I used to live just south of the mall off of 22nd st. next to the project homes. We didn't have any problems as we kept to ourselves. Any apartment complex targeting students will have a 6' fence and gate surrounding it for safety. If it doesn't, your car had a better chance of being broken into.
If your budget allows, look into the Carrolwood area as there are apartments around there or closer to I-75 off of Fletcher. Or maybe get a room mate and rent a cheap house in Lutz. That might work, too.
Carrolwood off Gunn Hwy. has decent places to live...good bars also