Just an option, not the norm:
Water taxi to Belize $US25 r/t pp.
1. Check out Old Belize Museum, my wife and kids loved it Old Belize Museum
You'll need a quick taxi ride (4 miles out of BC).
2. Goverment House aka House of Culture, former residence of the British Governer General, the Queen stayed here.
3. Museum of Belize, formerly Her Majesty's Prison. Very kewl tour! Great exhibits including a remaining portion of the old prison. Museum of Belize
4. St. John's Cathedral, Mosquito King's once were anointed here. (next door to Government House).
Other ideas: Belize City