I use the Garmin Edge Touring Plus, and get about two long days of touring out of one charge. If I go longer than that without access to an electrical outlet, I simply plug the thing into a solar charger that I keep on my rear rack, strapped to the top of my tent. Works well, and the Edge Touring is as fully-featured as a typical car GPS unit.

I mainly use a GPS-enabled computer because I want to be able to accurately track my milage and route. If you don't care about that, and don't need turn-by-turn directions, then I'd do what the other posters have suggested - go with a basic CatEye computer. A watch battery will last several months.