I think you will love going to Jekyll Island. One great option at Jekyll is to rent one or more of the "cottages". These are private homes, but they are all beautiful and very well appointed. You also enjoy full guest services (cleaning, making the beds) just as if you were staying at a hotel.
Jekyll Island has some nice golf packages. You might want to check and see if one fits the bill for you:
http://www.jekyllclub.com/packages.asp?id=48
If you have time, drive across to Sea Island one day while you are there, either for golf or just to see it.
Have a great time!