We've been visiting HHI since buying into the resort (HHI
DVC) in July 1997 -- had 3 kiddos at that time and added #4 the next year. Over the years these have been our favorites -- with the more adventurous ones coming in the recent years when the kids were older (now 26, 24, 19 and 17).
Day trip to Savannah is great (just really hot if you go in July or August) -- do the "trolley" tour where you can get on/get off to view the various sites. Easy drive down and back (take the back roads for better scenery along the way) and easy to fill 4-5 hours. Or skip the trolley and just grab a spot down by the river and start walking.
Further than Savannah but closer to Charleston -- day trip to Beafort. Another pretty little town -- but no where near the # of historic sites/buildings as either of the other two.
Day trip to Charleston -- further away than Savannah but another great day trip. Add on a tour of Ft. Sumner and/or the Navy ships.....good day. We've done a harbor cruise there too on a sailboat -- very fun
Old Town Bluffton.....nice small local shops, good eating (no chain restaurant stuff here) -- easy to walk around and explore and just off the island. Other than the gas to get you there and back and your meal - it's free. This is a place my wife and visit.....kiddos just not into it.
Kayak tour either thru DVC or on your own - about $20/hour for a 2 person kayak. We usually rent from Shelter Cove. Have also rented pontoon boats (when the kiddos were younger - about $200 for 2 hours -- do it over lunch and pack your lunch for a water picnic) and went out looking for dolphin on our own -- usually successful. We've never done a "tour" -- we've always just gone out on our own.
Recent must do things have been a Family Ski Day offered by a few outdoor places further down the island. Usually 4 hours out on a speed boat with a driver and the kids take turns water skiing, knee boarding and everyone's favorite tubing. You can bring you own lunch too. This is the priciest -- but does allow up to 6 people to go out -- going to be about $500 with a tip. Not an every year thing for us but has been THE #1 thing the kids talk about each trip. We have hours of Go-Pro video from these trips.
It's great to have some ideas before you go but also -- if you are staying at DVC HHI -- see Mike the "pool guy." Mike is a local and has over the years given us booklets or home made maps to local things he suggests doing.
Enjoy.