Yeah, U.S. dollars and Belize dollars are accepted with equal fervor anywhere in Belize. I usually bring traveller's cheques as a backup in case I lose my cash, credit cards and ATM card. TCs are accepted at most places a visitor is likely to go, though not in small shops and restaurants off the beaten path.
Now that ATMs at Belize Bank accept foreign issued ATM cards on the CIRRUS and PLUS networks, it's easier to get cash (they dispense Belize dollars).
Belize Bank isn't in Placencia or Caye Caulker, however.