If you really want Fabulous then try a place called Stripes, An American grill. It's just past the circle on the left...It's really terrific food. It's a chef/owner and he's a graduate of Culinary Institute of America and really does spectacular dishes. The portions are generous to say the least. You will not be disappointed. Probably the best Steaks I've ever had, my husband had a lobster pot pie that was beyond fabulous unlike any pot pie you've ever seen and TONS of lobster meat and I once had a pasta dish that on it's own was yummy but then it had 13!!! of the largest best shrimp I've ever been served. I can not say enough good things about this place. I recommend to everybody I know that's going to hilton head and they all agree it's one of the best restaurants they've ever eaten at.
Also tried Santa Fe Cafe, it's almost directly across the hwy from the resort. It's kind of an upscale southwest restaurant. It was really good and I've added it to my Must do list when we return.....
You'll get lots of opinions and there are lots of great places to eat these are just 2 of my favorites.