I am by no means a Panama expert, however I've put a lot of planning into our trip there next month. Have you looked at spending time in Boquete? They offer three of the four things you're looking for, minus the beaches however those are accessible about an hour outside the city. Most of the places, especially the B&B's are easily under $200 a night. Rent a car, but definitely read up on the mandatory rental insurance requirement for Panama, it will add about $20 a day to your rental car costs.