We LOVE HHI. It's such a neat resort town. It may be very chilly that time of year and difficult to do any swimming. You could probably still golf though and enjoy the beach from the shore, or even take a ferry to Tybee or Savannah to explore. The closest "big" airport is the Savannah/HHI airport. It's off the interstate, about 45 minutes away or longer depending on the tourist traffic headed onto HHI. It's not a bad drive usually. Saturdays are very congested on/off the island since most of the rentals rent Saturday to Saturday. There's a small business airport on HHI, but I'm sure it's crazy expensive to fly there.
A good time to go is May, after the big golf tournament in April, but before the summer crowds hit after Memorial day, HHI is very quiet then but also warm enough to swim. It can be really hot in May, but typically it hasn't hit the really horrific heat of July/August. I love going in May and have been the last two years.
The Disney HH DVC resort is very nice. We stayed there last year. My ds loved the pool and all the activities. The lifeguards knew him by name and were so sweet to him. The resort isn't on the ocean side of the island. It's on the "creek" side, next to Shelter Cove, but just a short shuttle/bike/car ride to the Disney Beach House on Palmetto Dunes. We rode our bikes over to the beach in the morning and then hung out at the main pool all afternoon. The Beach House has a small pool, too.
We also like staying at Sea Pines. There are lots of different lodging choices there...hotel, condo, houses, etc. You can ride your bike all over Sea Pines and explore old plantation ruins and other historical areas. It's a beautiful resort.