Yes, it’s easy to travel to other Central American countries with a U.S. passport. All those countries offer tourist visas without any prior arrangements. You get your stamp at the border. But you’ll probably need some sort of proof of travel back to the U.S. or other country, say a plane ticket back to the U.S. or a bus ticket out of the country you’re entering.
You have some options:
TransNica can get you to and from Nicaragua (Granada, San Juan del Sur, Managua) (http://transnica.com)
TicaBus can get you to Panama, Nica, Mexico, and other countries (http://www.ticabus.com/esp/)
Getting to Belize would probably require changing buses somewhere. It’d be a long trip.
Both of these companies have very modern, air con buses. Very comfortable. You don’t have to change buses at the border and the “crew” take care of getting your passport stamped and such at the border. As far as time, I’m not sure the calculation. But you can find out how long each route would take.
There are also lower cost bus lines in CR (Like Central Line, which has a station in downtown San Jose) that will get you to the border with either Nica or Panama. Then you have to switch buses after you cross the border.
I’ve always felt safe traveling along in Costa Rica, Belize, and Nicaragua. I know Panama and most of Guatemala is safe too. But I think parts of Honduras and El Salvador are iffy. I would consult guidebooks or online forums for tips on those countries.
.
