The currency system in Belize is fabulously easy for American visitors.  The Belize dollar is locked at $2 Belize = $1 US.  So it's very easy to see how much something is costing in US when you go shopping.  Most accommodations and tours are listed in US$ prices, and most restaurants, shops, etc. are listed in BZ$. Make sure to verify if prices are in BZE or US though, about 80% of them may be BZE in touristy places and 20% in US.  Seems like they're trying to make it easier, but it just ends up being confusing.  

Nearly everyplace (both inland and on Ambergris Caye) readily accepts US currency.  They also should accept traveler's checks as long as you write your passport number or driver's license number on the back.  However, don't bring large bills (anything above a $20) because $50 bills are rarely accepted (unless you want to spend $45).

ATMs are also available in most tourist destinations now - even Placenica, which now has 3 banks with ATMs that accept international credit and debit cards.  Other ATM locations include Punta Gorda, Belmopan, Dangriga, Belize City, SAn Pedro, Caye Caulker, Orange Walk, San Ignacio and Corozal.