Most places accept US Dollars as the Belizean Dollar is pegged to the US dollar at 2BZD = 1 USD. If you are traveling to the cayes, stock up on your cash at the central bank, as the ATMs on the islands often run out of money on weekends.
If you want to shop there is tourism village in the Fort George area which has jewelry shops like Diamonds International and lots of gift shops. Fort George is located on a boardwalk.
There is a cruise terminal there that receives Carnival Cruise Line ships.