Last time we were there '02 couple nice places. You'll be fine. Definetly one of the most connected countries in the world. Enjoy and try to stay away from computers for a few days
Caye Caulker has DSL and dial up through BTL. Although, with dsl available, I don't know why anyone would want to use dial up anymore, unless they were only on for a few hours a month. There are two internet cafes on Caye Caulker, both are located on Avenida Hicaco (Front Street) and within about 2 blocks of each other.