Check with your credit card company to see what there policy is on foreign exchanges. (Mine really stinks, they charge me a foreign exchange fee if I buy something online from a foreign country even if the charge is in US dollars).
Check with your hotel to see if they will exchange traveler’s checks, or if there is a bank nearby that will, as some vendors won’t accept traveler’s checks. Also find out what the exchange fee each charges. Sometimes the hotel will give you a better deal than the bank, sometimes the bank is the best bet. I think in Belize US currency is accepted almost everywhere, but it has been a while since I’ve been there.
Also, check out Belize’s tourism website. They may have some helpful information about currency, etc.