If you walk around Belize City either do it in a group of at least four big men, or make sure you have nothing of value on you. Especially but not exclusively at night. I was told once by the superintendent of police how many violent (gun) robberies there had been in Belize City in the previous 24 hours, and it was horrifying. Not to say you'll necessarily have something happen to you (I know people who've walked there quite safely) but the odds aren't good.