Without rushing to see it all in 1 trip: here some places I selected so far:

week 1: flight from San José to Caribbean coast:  Puerto Viejo de Talamanca for its beautiful beaches, Cahuita for snorkeling, the Gandoca-Manzanillo wildlife reserve,

week 2: travel by shared shuttle to Monteverde for guided hikes, hanging bridges and ziplining, will I dare?

week 3: Manuel Antonio and pacific coast: national park and beaches, guided tour in the park, playa ballena