For Scuba, IMHO you're better on the Gulf of Mexico side as oppossed to the Atlantic.
Naples, Captiva, Anna Maria Island all get good reviews but are pricey.
I know you've been to Miami but we stayed our last couple of days in the Art Deco area of South Beach and I thought that was really a "fun area" but not sure it's best if you're with smaller children. My 13 Yr old loved the shopping and the "buzz" of it.
If you want to relax and chill at a really nice resort then Disney's resort at Vero has a great pool, good activities for kids and a lot of nice restaurants about 15-20 minutes drive away. The food at the hotel is outstanding, but Disney prices.
If you're looking for a resort for a week, then you do have some places that are a little further away, but nice resorts. St Augustine on the North Atlantic coast gets great reviews and is about 4 hours away. If you don't mind a 6/7 hour drive then Hilton Head in South Carolina is a great beach destination. Disney has a resort there which I thought was wonderful, but there are a number of other resorts in the area. There is some interesting history and places to see in South Carolina and it makes it a slightly different holiday. It's something I'd certainly consider if I was looking for a destination for a weeks break.
