Panama City has lots of interesting things to see and do, so don't leave it off your itinerary when you are planning a visit. Your may want to tour the Canal or visit the Old Town. Here are some suggestions for your city stay.
Judy Tovar of East Travel Panama is a terrific guide. She grew up in Panama and went to school in the US. Her English is excellent and her knowledge of and enthusiasm for her country are unparalleled. Judy's email is: easytravel@cwpanama.net.
Some hotels we have used are (listed from least expensive to most expensive):
Marbella (very basic, economy)
Sevilla Suites (quite comfortable and spacious, some rooms have kitchenettes)
Bristol (a very nice hotel)
The above hotels are all in an area called "El Congrejo" where you can find numerous good restaurants and shopping within walking distance.
Things in Panama City can get booked up quickly, especially during high season. So make your airline and hotel reservations as early as you can.