Overall, Tallahassee has a small-town feel and is relatively safe. The crime rate in Tallahassee near the colleges is quite smaller than in other outside areas. Most crimes in Tallahassee are petty crimes like breaking into homes while students are away or busting the windows of parked cars. There are a few parts of town where you want to keep your eyes open like Frenchtown, which is just a few blocks outside of the FSU campus, and certain parts of Southside.
If you have any concerns for your safety, get to know your local authorities. There is the FSU Police Department, Tallahassee Police Department and Leon County Sheriff's Office. All are at your beckoning call to protect and serve you and your community.
In the case of an emergency, always call 9-1-1 and know your non-emergency numbers, too! For TPD non-emergency calls dial 850-891-4200, or you can even report a crime online! For FSU PD non-emergency calls 850-644-1234 and for the Leon County Sheriff's Office non-emergencies dial (850) 922-3300.
Like anywhere else, pay attention to your surroundings and you will be just fine. We have a ton of resources on RentTally to learn about apartments in Tallahassee and surrounding neighborhoods.