Take a look online at these,
islands of Boca del Toro
Isla Barro Colorado for wildlife
Panama City- if you want the urban experience
Boquette***
San Blas Archipeligo
I think the best thing to do is decide what you'd like to see and then map out a practical route, check out transportation options (probably mainly bus) and see what's going to be possible to cover in your three weeks without powering through.
Here's a
Top 10 Best Attractions in Panama City to check out
And
Best Natural Attractions in Panama