I was going to suggest Monteverde also. From SJO, one can get a shared shuttle for about $52us - the bus is cheaper, but you have to get from the airport to the bus station, and the scheduling is less flexible.
Once there you can stay reasonably. e.g. in Santa Elena village there are several hostels - I stayed in one that was perfectly comfortable with a private room and hot shower for $15/night.
Also check out AirBnB - one place we stayed, and can recommend, is Hummingbird House in Monteverde. It is adjacent to Reserva Bajo del Tigre and an easy walk to my favorite reserve, Reserva Curi-Cancha, and also to the Monteverde Institute's reserve. One can also easily walk to Monteverde Reserve (perhaps the most famous of them), though it is about a 4km walk mostly uphill (downhill on the way back, though!). There are good restaurants right there, and a small grocery store. It is also easy to walk from there down into Santa Elena for the evening, and if you prefer, take a taxi home after dark. Another great reserve, Santa Elena, is farther but can be reached by public bus or taxi.
The nice thing about this area, is that even though these reserves are in close proximity, they differ in habitat and altitude, so the chances of seeing a wide range of species is good. Monteverde and Santa Elena are on opposite sides of the continental divide, Curi-Concha is recovering secondary forest and often the most productive (and great for Resplendant Quetzal in February and Three-wattled bellbird in March (Bare-necked Umbrellabird made a few appearances there last April, too). Bajo del Tigre is pre-montain cloud forest.
Enough rambling. In full disclosure, we stayed at Hummingbird House on our first trip to CR, and have become good friends with the host family - we will be staying in another part of their compound this coming February and March.