"Old Belize" is pretty decent too.....restaurant, bar and a small museum attached in the same complex:http://www.oldbelize.com/
charter a taxi (very reasonable) and spend a few hours there
(Taxi suggestions, contact in advance the GREAT drivers listed on my taxi page, they will provide some history and answer questions on the way as well - http://www.belizecity-daytrip.com/taxi
P.S. have a great time, Belize City is great once you know what to expect!