A nice advantage that Panama has, even though is a small country, it has a lot of things to offer, beautiful destinations.  You could easily go from Atlantic to Pacific ocean in just 3 hours, so you can imagine.
These are the provinces you should look at: Chiriquí, Bocas del Toro, Central provinces (Herrera and Los Santos).  I live in Bocas, for me the best! 
Panama City, is a big city, I grew up there but after leaving in the country side for almost 15 years, I do not want to go back to the city, although for new visitors, you cant miss the Panama Canal.

A lot of families, travelers come to Panama to learn Spanish while they enjoy their vacation.  This website has a lot of information about locations I mentioned above: [Habla Ya Spanish School](https://www.hablayapanama.com/?utm_expid=1303580-10.1FpanowBQw2DIM4PIIyE7g.0)

_For how long?_ It all depends on how many times you have the chance during the year to travel for vacation.  I think you could easily enjoy a lot of things of Panama in 1 to 2 weeks.  And if you prefer to travel for more time than that, you should also take the opportunity to visit Colombia, since there are economical flights from Panama.