A good guidebook to Panama would serve you well at this point. It would help you clarify a lot of these very general questions you have.
PTY is quite far from Panama City. By the time you factor in immigration and customs and the need to get to the bus terminal, you will have nowhere near four hours to kill.
No one spends much time in David. It's a hot, sweltering, small, business-oriented city. For me, the real attractions in that area are Boquete and Volcan and Cerro Punta, all about 90 minutes north of David. All are at higher elevations (3,000-6,000 feet) and are much cooler. There are a lot of great hikes in that area. That's my favorite part of Panama. All have some decent budget accommodations too.