The ruined old city can be seen fairly well by driving through it. Casco Viejo is not terribly large, and it suffered calamitous fires until the 19th century, so the surviving (and rapidly gentrifying) neighborhood looks more than a bit like New Orleans, with French-style balconies.
You didn't say where you'll stay in the city. If in the Via Espana area, good food is everywhere. Madame Chang's (near the huge Marriott) is elegant, excellent, and affordable.
If you can find or organize an excursion to, say, Chagres National Park, it would be worthwhile. It's the dry season ("Verano") and the forest paths are inviting, and reasonably likely to be free of chiggers (the local remedy is the same as in Florida--dust yourself with sulfur powder around the ankles, waist and neck before going out).
Tocumen airport has a tiny government-run craft booth with nice basketry and excellent prices.