Down town Belize City - Just be careful where you go. There are some areas that are simply 'No Go' areas for the tourists.
Walking out on your own can be a bit dangerous, so make sure you are always with someone.
Belize City. I don't what there is to see there. It is very dirty. I only stayed there one night and someone tried to break into my hotel room while I was sleeping, woke me up. It was the Holiday Inn.