Freedom City is where your character will start the game once it has been created. Freedom City has many shops and public service outlets which can be of use to you immediately. If you haven't already, you might want buy some armor and weaponry. Although Freedom City isn't terribly dangerous, there are some perils. Most of Freedom City is, however, protected by the strong officers of the Freedom City Police Department.
You are able to purchase an apartment or room for yourself where you can disconnect from your character without fear of being killed in your sleep. Most of these places have security systems to keep burglars and would-be assassins out, but none of these systems are foolproof, so you might also want to invest in a safe of some kind.
The area directly outside of the FPCD defense perimeter is known as Slagtown..
Slagtown is a little seedier and more dangerous than Freedom City, and is, for that reason, not protected by the Freedom City Police Department. Once you venture outside of Freedom City, you'll be responsible for your own defense.
For your convenience, a map of Freedom City is included in this page.
A detailed map with descriptions can be found here.