We spent a week and a half in Panama a couple of summers ago. We could have happily filled more time there, but that was the time we had. We didn't transit the canal, but we took a cruise on Lake Gatun as part of a guided hike. We also saw the locks at the museum near the city. We went out to the Azuero peninsula (with many interesting stops along the way), which was the departure point for our guided camping/snorkeling/hiking trip on Coiba Island. We ended with three nights in El Valle. There were other places we were interested in, but didn't have time. I can easily imagine filling two weeks just by extending time at the places we went, not even adding other stops. We plan to return.
We rented a car, but didn't drive in the capital except briefly to get to the hotel. It was a little hairy. But leaving the city and driving elsewhere in the country was very easy.
If you drive southwest through Capira, don't miss a stop at Quesos Chela for empanadas and chicheme (a drink). We stopped both times we passed.