We visited HHI for the first time a couple weeks ago, and loved it.
First of all, if you are at all into bicycling, I highly recommend that you rent a bike, probably for your length of stay. There are paths running along most of the roadways, but even more glorious is the fact that the sand on the beach is packed tight enough to allow biking on the beach. You can access the beach via the pathway on the left side of Disney's Beach House. Lots of places on the island rent bikes, but most of the cruisers seem about the same quality, so you are probably best off to rent throught Disney.
Good food abounds in HHI, our favorite meal was probably the the Old Fort Pub. Pricey, yes, but well worth it. And if you are lucky enough to be seated durning sunset, it's gorgeous. We also enjoyed the Old Oyster Factory.
We second the vote for Captain Scott's Dolphin cruise, it was one of the highlights of our trip.
Finally, we were fortunate to have a marsh view for our stay, and it really was nice. There were a couple of times that we spotted dolphins from our balcony. And for a few memorable minutes, a large hawk landed on the live oak just outside of us; until he was chased away by an aggressive blue jay!
Enjoy your trip!