Belize City's bar scene is modest but real. The local drink is Belikin beer — the only beer brewed in Belize — served ice-cold everywhere. Rum is also ubiquitous. Cashew wine, brewed from the cashew fruit rather than the nut, is a local speciality worth trying if you see it; it has a mildly fermented, fruit-juice character that's unlike anything else in the region.
The better hotel bars in Fort George — the Radisson and a few guesthouses along Marine Parade — are pleasant spots for an evening drink with harbour views. The area around Southside has rougher bars that locals favour; these are fine during the day but require more caution at night.
Eva's Bar has long been a travellers' institution, known as much for its noticeboard of local information as for the drinks. It's a good place to find out about transport options, tour operators, and where other travellers have been.