Re: Hilton Head / Savannah GolfI go to HHI annually with family. Golf isn't cheap there in general, so your price range may not be realistic unless you drive pretty far off the island, esp during Heritage week i'd imagine.
My favorite courses are at Palmetto dunes, esp the Robert Trent Jones course. Playable "resort course" at first gradually turns into quite a beast with tons of water, some forced carries/long Par 3's, etc. 10th hole par 5 is one of the few on the island (surprisingly) with an ocean view and you have gorgeous views from the green. The Fazio Course at Palmetto dunes is OK but a tougher test. I've not played the Arthur Hills there. They often do have multi-day packages esp if you're staying within the resort.
Favorite restaurant by far is Marley's, fun Caribbean-inspired food, cool atmosphere, yet also very family friendly. Red Fish is supposed to be excellent, although I've not eaten there as it's not exactly kid-friendly. Unfortunately there's a lot more in the way of mediocre seafood places on HHI, and everyone you ask will tell you a different place (I think Steamers in Coligny Plaza is fairly dependable, but certainly not outstanding). For comfort food you have to try Barbara Jean's, which has a location in Bluffton.