The Hotel Versalles is a decent hotel in the interesting town of Chitre. It is clean and offers excellent value, Internet access, a restaurant, bar, and a nice pool. It is only a few minutes drive to the desert of Sarigua National Park
This wonderful little resort at the southern tip of the Azuero peninsula near Pedasi is a jewel in the rough. There are currently only 5 rooms but they are building 8 more! If you do not like birds and wildlife in general, you will not like this place: they have birds roaming all over the place, including some chickens, parrots and a couple of emus! On the other hand you can also observe howler monkeys and sloths. This place is also a riot of different eclectic art pieces embedded in the walls everywhere, and the family that runs the place is wonderful. They have hammocks all over the place so you can crash with a good book and relax.
This place is also equipped for campers and you can setup a tent anywhere for about $8/day and use their shower and bathroom facilities. There is no hot water but you will not miss it as the water is lukewarm and feels good after a day in the heat. They also have a nice protected beach and they rent snorkeling equipment.
I hear this place gets quite busy with Panamanian families on weekends during the Panamanian summer (January to March), and with 8 new rooms coming up, the nature of this place might change.