Hilton Head Island has lots of grocery stores. I've heard vacationers say they pack coolers full of food to save money on their vacation.
You probably don't need to do this!
Check out the following grocery store websites for their weekly specials before you arrive:
Use zip code 29928 to search for the local bargains and best prices on what you need for the week. If you are arriving on Saturday the island stores can get very crowded and the instore delis sell out of cold cuts frequently. It's easy to stop in Bluffton before you reach the bridge and you are only about 20 minutes (assuming good traffic) from Hilton Head Resort and the island. You might want to grab a bag of ice just in case.
The Piggly Wiggly at Shelter Cove is the closest grocery store to Hilton Head Resort and is only 6/10ths of a mile and a 12 minute walk from our front gate.
There is also a Bi-lo, Sams Club and Dollar General about a mile north of the resort. Publix, Harris Teeter and Wal-mart are around mile marker #3 to the north and another group near mile marker #10 to the south.
And of course the Island Grill and Deli onsite in building one has a small variety of grocery items. They also provide takeout pizza and anything on the menu is available for pickup. Breakfast is served all day!