I stayed @ the Las Vegas Hotel by the Veneto Casino. Nice place. I literally walked all around that entire area (all the way to the water), felt very safe -- much safer and cleaner than San Jose (CR), almost felt like walking around Seattle. I'm sure there are bad neighborhoods of Panama City, but that area seemed very safe to me. Lots of high-rise construction too.
I've heard there are 'working girls' at the Veneto bar sometimes. Also heard about a place called Golden Times. Don't know any details, I'm married ;-).
The Multiplaza mall was quite empty, and not cheap. I've heard there are inexpensive places to buy things in Panama, but I didn't find such (didn't look too hard).