DH prides himself on having played every course (that isn't totally private) on HHI at least once. His "best buy" and the course he says is in best condition (at least later in November, when we go) is Hilton Head National, just over the bridge. He also likes the 3 across the way in Palmetto Dunes. I believe you'll get a discount if you ask at the front desk. Of the 3, Arthur Hills is the best. Fazio can be pretty tough for some people since each green is elevated and surrounded by sand traps. Don't expect to see much ocean on the Ocean Course-just a peek on one hole. Also, there are 2 courses there and DH has never been pleased with their condition-but then, he used to be an assistant greenskeeper, so he's pretty fussy. Some people like Indigo Run, but the 2 times DH golfed there, they treated him like such an outsider/tourist and weren't cordial at all. Same with Hilton Head Country Club. Can't help with the Charter Fishing-DH spends so much time golfing, he has little time for anything else.
Oh, I just remembered-if you get early tee-times, don't be surprised if you encounter "frost delays" some days. Although not every year, we have been delayed a few times because of frost on the greens.