OK, you need to go to San Jose, the capital city, but don't stay around to much, the best places are the small towns, the the mountians or the coast.
If you go to Costa Rica you NEED to go to: one volcanoe, two national Parks, one valley and the rain forest.
Volcanoe: Arenal in Alajuela, Irazu in Cartago, Poas in Alajuela (either one beautiful!)
National Parks: Manuel Antonio in Puntarenas (beach) and Braulio Carrillo in San Jose (rain forest)
Valley: Valle de Orosi in Cartago (stunning views)
Rain Forest: Monteverde (go cannopying!!!!! is the best!!!!)
As to where to stay, there are lots of places, cheap ones, and expensive ones, B&B, chain hotels, guest houses... I suggest you visit this website:www.visitcostarica.com, that's the official wesite.
I hope this helps! have a great trip!