What a question!!! There is SO much to do here...
Let me try to summarize a few of my favorites. I've lived here as a kid... and, now as a 51 year old adult, and I don't know which is more fun.

With kids (teenagers):
Rent waverunners and go for a 1/2 day ride - it's amazing, and you WILL see dolphin
Rent a pontoon boat and cruise to the end of Shell Island - it will take all day - pack a picnic... swim, snorkel, go crabbing and floundering.
If the teenagers want to meet other teenagers, there are lots of places to do that - Shipwreck Island Waterpark is a great place to spend the day.
Go to Spinnaker for lunch and hang out on the beach.
Go to Schooners for lunch or early dinner and hang out on the beach.
Go to Pineapple Willies... same thing. The adults can grab a waterfront table, and keep an eye on the kids strolling/playing on the beach.
I hear Rock It Lanes is fun, too, and there are lots of amusement rides, etc....

Hope that helps!