The province of Chiriqui offers a lot of outdoors activities as many others have commented. You can also go to Boquete for a coffee tour, canopy, hiking, and rock climbing. I recommend Boca Chica in Chiriqui, approximately 6 hours from Panama City.
You can trust that Best Places does not manipulate content to sell you anything. All opinions in the Community Q & A and Expat Stories are those of its authors, not Best Places.