Most places do take the major credit cards. We were there during the BTL strike (telecom company which services all of Belize). During that time, since phone lines were out and transactions couldn't process, we used mix of US and BZ cash. Traveler's checks (AMEX) are useful as well. When you arrive at BZE, there is a currency axchange desk conveniently located in the airport after you go through customs. You will be amazed how quickly you learn to pay for things with a mix of dollars.
An aside: our snorkel guide liked to express his age in US "currency"...his 32 years made him only 16 BZ : )
Take more than you thing you need! There's lots of fun things to purchase, and it helps boost the economy, especially for locals who sell handmade lovelies.