SJO (Juan Santamaría International Airport) or LIB (Daniel Oduber Quirós International Airport)
Yes, there are two airports that will get you to Santa Teresa from San Jose. Tambor (TMU) and Cobano (ACO) will get you there in under an hour.
We recommend renting a car for the journey getting to Santa Teresa. Once you are there the town is very walkable.
If you aren't able to get a room at the suggested hotel, we highly recommend looking at accommodations through Air Bnb, Hotels, and Hostels.