Florida is next door. Well, it is about 800 km to Orlando and significantly more to Miami, Everglades and the keys. Still, it is our favorite place for short trips. Looking back at a number of trips (including earlier ones without kids) now I conclude the following:
1. Disney: Kitschy? Yes, very much so. Expensive? Kind of, too. Still, I would not want to miss the memory of Hannah greeting her fairytale idols (Cinderella, Sleeping Beauty in particular). If you are around, you must go to Disney. Even for adults it is fun, with some planning you get a lot for your buck, I think.
2. Beaches: I never liked the beaches I knew on the Atlantic Coast (Miami Beach for example). On the Gulf coast, beaches can be great. I tried Sanibel/Captiva (shell collectors, not sure about swimming); St. Pete and Clearwater (crowded, but quite good and of course good infrastructure). The panhandle (Ft. Walton Beach, Pensacola) had great soft white sand -- good to visit when it is too hot in main Florida. Sarasota (Siesta Key) was overall most impressive (infrastructure, not crowded, very nice beach). If you look for a bit of everything - Siesta Key would be the place I would like to visit again.
3. Culture and Sights: Everglades and Keys are most impressive. St. Augustine is a very pleasing change to the european eye, but at the same time not that special when coming from Europe. Engineers, IT geeks, school boys and the like probably must see Cape Canaveral.