We have been to HH three times and I used to live there. Anything that Christopher does (he is the naturalist) is great. Most are also free. Probably not appropriate for a 1 year old, but my 8 year old and I really enjoyed the bird walk and Chris did a science program, Mission to mars that 2 40 year olds and 2 8 year olds enjoyed. Also, don't miss B'lu (sp.) crabbe at the resort. He is the entertainer and is one of the best things about the resort. THe campfires also are fun. After comparing HH and Vero's campfire, I definitely give the edge to HH. Off isalnd, are some serious shopping facilities. The outlets in Bluffton are good, about 120 stores including Wedgewood, Oshkosh and others. Also, being so close, I would plan a day trip to historic Savannah or Charleston if you can. Savannah has a midnight in the Garden of Good and Evil tour ( I think they still have it) and Charleston has a good ghost tour plus wonderful places to eat. Savannah is about 45 minutes, Charleston about 1 1/2 hours.
For eating, I recommend the brunch on Sunday at Edible Pursuits. Lots of food including make you rown omelet for about $6.99 per person. I did not find Giussippi's to be quick or good, so I personally don't reccomend it. The Kingfisher is good, but expensive. There is a good mexican restaurant across the bridge whose name escapes me at the moment that we go to a lot. Aunt Chiladada' down by the circle has all you can eat crab legs still, I believe if you like crab legs. My mom also reccomends the HH diner for breakfast. There is a little french bakery in the Pineland Mills shops that you should definitely try for lunch and bring home some desserts as they are great.
Hope this helps, enjoy your trip it is wonderful at the resort. After reading the posts on this board for about a year, I can't remember one negative post about HH.