How far and how long will it take to get to cahunta from san Jose? Are there van pick ups from airport to hotels in cahunta? Taxi's?
Do you mean Cahuita?
Taxi from SJO might be too expensive.
We took Interbus and PleasureRiderCR shared shuttles. About US$54-59 pp one way, shared van, with a/c, needs to be prepaid. E.g., for Interbus, see rates and estimated travel times here: https://www.interbusonline.com/rates.php .
There is also Caribeshuttle. It has lots of TA reviews, but we have not used it.
The Interbus one leaves at 2:30 pm, and by then, you need to get out through the customs and get a short taxi ride to Denny's parking lot, which is Interbus and Caribeshuttle vans pick up, if you miss your prebooked shuttle, they leave, keep your $$ and you need to look for an alternative.
http://www.pleasureridecr.com picks up right from the airport. But if you are travelling solo and they do not have anyone else booked on that date, you would need to buy two tickets, or they won't book you.
The shuttle times may not work with your flight time.
You can also take a public bus for US$10, about 4.5 hrs for the direct bus (vs the route via Limon), but you need to first get to the correct bus terminal in San Jose (the same bus cannot be taken right from the airport). See the first link above for the exact location of the terminal and the schedule.
You can also take a private transfer - a driver with a car will meet you. Your hotel in Cahuita might arrange one for you or see Travelling Options under the Top Qns about CR on the right side of the screen on the main CR forum - there are many links for private drivers. If might cost you about US$200 one way (we had also been quoted much more, depends on who you contact and the exact destination).