You can get some good deals on vrbo.com for condo rentals. I would look in the Thomas Drive area -- Dunes of Panama, Pelican Walk, Hidden Dunes, ones in that area.
Go to Coconut Creek Mini-golf and Gran Maze. For a set price per person, you can play unlimited rounds of mini-golf (2 courses) and do the Gran Maze as many times as you want until 5:00 the following day. The website has coupons for $2 off the price.
If you head to the main part of Panama City (across "the bridge"), you will find more reasonably-priced restaurants and most of the familiar chains, plus local places, too.
Pier Park is a new, big outdoor shopping area. There's a merry-go-round there and you get an all-day pass for $5. There's a really nice movie theater there, too, The Grand. They do summer movies for kids for a very reasonable price, like $3, including a small popcorn and drink.
There's a huge recreation park called Frank Brown Park near Pier Park. There's a nice playground there, and a water playground, too (admission to that, but I think it's reasonable).
Hope this helps!