Hotel in Panama City

In that price range (including taxes in your $60 limit), I'd go to El Parador: http://www.hotelparadorpanama.com/
Note that ALL hotels in Panama City are very, very full this time of year -- so try to book well in advance.

On the back and environs of the Hotel El Panama there are some hotels and a lot of back pack hostels. I stayed once at Torres de Alba just across the street of Il Pommodoro (exquisite pasta, went there almos daily!)... This is downtown hotel district "El Cangrejo", without being in the run-down downtown area. I also stayed in Apart Hotel Sevilla or something like that is half a block from there, on the street that comes from the Panama University. There were also hostels half a block from the Hotel Riande Continental, where 6 to 8 backpackers per room bunked together, also Internet Cafes, etc. I walked a bit to the Marriot and across the street there is middle-eastern food.

TRY THE LAS VEGAS SUITES, IN THE SAME AREA AS DESCRIBED ABOVE.

Las Vegas is a little bit more expensive than the Parador, does not have a pool, and traffic noise there is a real problem. Plus, I think the wine bar and restaurant is overpriced and vastly overrated. Just my opinion, of course... :-)