I've lived here a couple of years now. You have many food selections on-island depending on your taste and budget. Most will be very crowded this week.
The Shelter Cove Marina area has varied selection of restaurants. There is a large public area behind the shops, and there are many family oriented activities planned this week.
Salty Dog in Sea Pines is very popular and also has a large outside dining/bar area, and shops to keep you busy while waiting for a table. Very touristy, but good.
For beer, the Lodge has the best selection. A few local selections, but many more on draft. Its located in a complex just off the main traffic circle. In the same complex is the Hilton Head Brewing Co. Their beer isn't my favorite, but they do good business, so you may enjoy it. There are a few other restaurants in that complex, and all are predictably good.
Off island, but reasonably close, the best on-site brewed beers in the area, IMO, are RiverDog Brewing and Southern Barrel Brewing. Both located in the Bluffton area. RiverDog is a tasting room, that serves small plate food. They offer a small batch beer each Friday. Last week they had a Dobblebock stored in red wine barrels. They also have the best sours that I've found in the area. Southern Barrel has a larger dining area, and more beer selections. They are also very good.
Don't forget your umbrella, looks like a chance of rain every afternoon this week. But being from Tampa, you may know what that's about.