Belize City, Belize
I'd stick to the tourist and resort areas. Belize is a poor country, which means theres some places you wouldn't want to be at alone. San Pedro is a pretty safe place but Belize City does have its unsafe areas.
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.