Tips on where to go outside of PC itself? Go check out FORT LORENZO. On the Atlantic side. An old Spanish Fort. Been invaded by raiders such as Sir Francis Drake, Pirate Henry Morgan.
Check out EL VALLE. Nice mountainous village outside of PC about an hour and a half away.
Check out BOQUETE out near Costa Rica border, about an 8 hour drive from PC or if you fly to DAVID, its only about less than an hour north to Boquete.
If you like the beaches, check out Coronado, Gorgona, Santa Clara. All beach areas. If you want to check out the SAN BLAS islands, it's a hop by plane. Don't know the details of the cost.
Or just hang out in PC, play the casinos, go eat in nice restaurants, just walk around, its neat. Check out the Hard Rock Cafe at MULITCENTRO.
Check out PANAMA VIEJO. They have a museum, and its the site of Pirate Henry Morgan's invasion of Panama City in the 1600's. It was burned down by the residents before they left the town. You can see the old ruins coming from the airport. Check out the Panama Canal Museum at MIRAFLORES LOCKS. They have a FRENCH version of the Canal down town too. They have a gift shop where they sell Guayabera's and other things in all of these places. Night life is the norm in PC so dress accordingly and have a few beers or rum and cokes. Not a place for the lame hearted.