For Tikal, from San Pedro you're probably going fly (Maya Island and Tropic both do the trip).
Most hotels, fancier restaurants, most tour operators and larger shops accept bank cards, sometimes with a 5% or so surcharge. No need to bring any Belize dollars. US dollar are accepted everywhere in Belize. In Guatemala it's handy to have quetzales, although US dollars are accepted in some places and Guatemala is looking at dollarization.