FAMU requires its first year students to live on-campus. If you're past your first year, or you are coming in and can be exempt from this requirement, an apartment near FAMU can be a great option for you.
Choosing where to live is a big decision – not one you want to have to make at the last minute or simply do what everyone else does. Also, returning students start choosing their dorms during the Spring semester. If you do decide to apply for a dorm, you will want to get your application in as early as possible.
You can generally find an apartment near FAMU a bit later than a dorm and still have a nice selection available. That said, a big consideration in choosing where to live is often price. FAMU dorms differ for each hall, so your price depends on how much your particular hall costs. When I was deciding between living in a dorm and an apartment, I divided the price per semester by 4, because you will be in your dorm for about 4 months per semester. This gives you a good estimate of your price per month in the dorm, and makes it easy for you to compare to apartment prices by month.
When comparing prices, make sure to take utilities into account – your dorm will include these in the price, but a FAMU apartment may or may not include these in the rent. If they don't, talk to some other people who live there and ask what they pay for utilities. If you don't know anyone, you can ask who your water, electric, and trash providers will be, and then either visit their websites or call. They can generally give you a pretty good estimate based on the approximate size of your future home.
If you choose to live in a FAMU apartment, you will probably sign a year-long lease. If you want to go home for holidays, the summer, and maybe even some weekends, you will be paying for time that you aren't living in your apartment. In a dorm, you have to be out of there by certain times. If you want to have a job in Tallahassee, and plan to spend most of your downtime there, an apartment makes more sense.
Space is on big difference between living in a dorm and an apartment. Dorms are generally going to be smaller, and often do not allow for much cooking to go on in your room. You will also not be able to bring as much of your furniture. Conversely, if you don't really have much furniture – you don't have to think about finding some. Of course, some apartments come furnished already, so this may or may not be a difference.
Living in an on-campus dorm, you will be closer to campus activities and your classes, which may mean you can sleep in a little later before your way-too-early class (This is one point that I have probably given more consideration to than anything else!) You may feel more involved living on campus, but living off-campus will allow you more freedom to find activities off-campus. There are pros and cons to each choice – what really matters is what you are looking for in your living space.