Panama City’s traffic is simply a nightmare!  We rented a car for a week and drove 600 km around Panama, but the driving into and out of the city (using el Puente de Los Americas), was bad.  We stayed at Tucan Golf resort, on the western side of the Panama Canal, where we could see huge ships crossing the canal to and from the Pacific Ocean.
We hiked into Parqueo Metropolinano (natural reserve within Panama City) and saw a sloth, Geoffry Tamarins (monkeys), a snake, many species of colorful birds, turtles and much more. 
The views over the city were amazing!

We visited the Miraflores locks and I found it was really touristy (and pricey -20$US/pers.- kids as well).  Nevertheless, the ''live'' explanations of the functioning of the locks and the 4000 massive container boats passing few feet from the observation deck was impressive.  A new (bigger) lock for 15000 container boat opened in 2016, but you can only see these boats at a distance.
We went hiking twice in Soberiana National Park (one morning, and one evening).  It appeared that the park was off the main tourist route and we saw many animals: howler monkeys, coatis, capybaras, dozens of blue morpho's butterflies, manatees, toucans and amazing variety of bird species, iguanas, etc.  The pipeline road did not stand to its reputation with hundreds of bird species, but the walk was pleasant, and the number of mammals per meter squared was very impressive.
We spent 2 days in Fallaron (Playa Blanca), to soak up some sun.  The beach was mostly black sand (and not white!) and the ocean was very refreshing.  It was really quiet as we were visiting midweek, but weekends seemed to be very busy.

We finished our trip visiting El Valle (Anton).  The aguas thermales (hot springs), were pleasant, but not very warm.  The best part of this visit were our mud facials we got before swimming!  The pools were nicely set in nature.  We visited the golden frog research center,
Overall, a nice relaxing sunny week, despite the city traffic.  Panama was a rather expensive country, with few sightseeing to offer.  Great for a short escape & great wildlife!