Depends on time of day. Do you speak spanish? Airport is not close to downtown, and traffic can be a bear.
Also, you will have to probably pay the tourism tax if you leave and re enter the airport.
That said, if you are dying to do something, grab a cab to the Mercado de Artesania in downtown, then walk towards Mercado Central, about a mile...grab a cafe on the way or eat street food. From there, you can get a cheap bus back to airport, or a $15 cab.
Gritty, memorable, can barely fit in 5 hrs and be enjoyed.
Sorry, no formal tour.
Just to get out of the airport, take a cab to downtown Alajuela or Herredia and get a licuado (milkshake/smoothie). about 8 years ago