If you’ve only got 3 days then you don’t want to waste your time traveling to and fro.  Panama City is worth spending a day, to see the Casco Viejo and the Canal; then get out of the city to the Pearl Islands (Las Perlas Archipelago), which are a 20 minute flight from Panama City, and about as far removed from urban life as you can imagine.  Contadora Island is the most developed of the Pearl Islands, with lots of B&Bs and little boutique hotels, exquisite beaches, great restaurants.  Both in Panama City and Contadora you have all kinds of budget options for your stay.  If you are more of the all-inclusive resort type, then you can also fly into Panama City and spend a couple of nights at a beach resort just outside the city – the Decameron, on Playa Panamá, is a popular choice.  They offer flight + stay packages that are reasonably affordable.