The Great House (moderate, around US$90) a night, is a fine choice in the Fort George area, which is safe. Twelve rooms in an old three-story colonial house. Good restaurant on the first floor.
In the international category (expensive --US$150-$200), the best is the Radisson Fort George. The tower rooms are raw, as my son says.
In the low-moderate category (US$60 or so), I'd highly recommend Colton House. It's in a safe area, right across from the Radisson and next door to the Great House. It's run by a wonderful couple, Alan and Ondina Colton. He's a former Brit soldier, she's Belizean, from Caye Caulker I think.
If you want to stay outside the city centre, Villa Boscardi is a wonderful B&B about half way between downtown and the international airport. About US$65 including breakfast and shuttle to the airport. In that same area the Biltmore Plaza is a motel that's fine if you get one of the newly remodeled rooms (US$75-95).
Belize First http://www.belizefirst.com/