Your suggestion of Brunch at EG or TH outweigh all of the dinner options suggested, IMO. The south location of Tupelo Honey will have less of a wait than the downtown location (you can even make reservations), or be prepared to wait at the downtown and/or at Early Girl. A few doors down from EG and our favorite brunch spot in town is Laughing Seed. Nice patio, usually no wait, local/organic/veg food, huge portions and decadent omlettes, pancakes and killer huevos rancheros.
If you need to shop for your cookout, Greenlife and Earth Fare and excellent grocery stores on par with a Whole Foods Market.
Whole Foods Market
3540 Wade Ave, Raleigh, NC 27607
12235 N Community House Rd, Charlotte, NC
Tupelo Honey Cafe
12 College St, Asheville, NC 28801
Laughing Seed Cafe
40 Wall St, Asheville, NC 28801