We stayed at HHI last August with two girls ages 6 and 10. Here's some stuff, in no particular order.
They especially liked playing on the beach. The beach starts with powdery white sand. Then there's a section of damp sand that's perfect for making sand castles, burying dad, etc. And then there's a part that is hard packed, and you can ride a bike on it. The 10YO in our group thought that was about the coolest thing she'd ever done. Plus there's two tides a day, so it's constantly changing.
The water was really calm, and it's shallow for a long ways out. We bought some cheap
WalMart boogie boards, and the waves were just big enough for them to think they were surfing. The water was real warm, too, but we went at the end of the summer.
There's all kinds of Dolphin tours around. I'd suggest a small boat, too. We went to South Beach Marina to set up a fishing charter, and took our dolphin tour with Commander Zodiac. Great fun!
The kids liked the Goyataku activity at the resort. That's where you paint a fish and press it on T-shirt. We took them both parasailing, and of course they thought that was awesome. But they were bored to death on our kayaking trip. That was our one disappointment.