Destin is my family's favorite place.
As said above The Back Porch is great, and is on the beach and the kids can play out there no problem (sometimes we go straight there after driving all day).
Seaside is great hopefully will be less crowded than it was this summer. Awesome place when not crowded. The Great Southern restaurant in "the circle" is one of my favorites.
Bass Pro is great with the kids, they have fish tank, a glass elevator. Love going and looking around since it is not something I do back home. Around holidays they have kids activities. There is a small playground area in that shopping complex too and a movie theater (for bad weather, never been though).
Fudpuckers restaurant is one of our kids favorite places. They have alligators, the kids can hold one and get a pic for $5-10. They have a small play area and Fat Daddy's arcade is next door, they just expanded it. My oldest kid LOVES that place.
The Track is a huge go kart / kiddie ride / mini golf / arcade that the kids will love. Do yourself a favor and eat at Merlin's Pizza after The Track (it is right by it). Wow it is great!
Henderson Beach State park is clean and has restrooms, we go here most days, especially if it is a busy time of year ($6-8 to enter). There are plenty of free public access beach points otherwise our favorite being the Crystal Beach access.
Baytowne Wharf has restaurants, playground, arcades and it is fun, but we don't go as much as we used to. Go if you haven't been.
Harbor Walk village is great, lots of boats docked, arcade, zip line, kid stuff,
It is a pretty long drive but St. Andrews state park in Panama City has the best snorkeling area.
Other restaurants we love: Pompano Joe's, The Whale's Tail (kind of a dive but right on the beach), Harry T's at Harborwalk, AJ's, The Surf Hut.
Have fun!