The Carolinas are a lot to cover. It is hard to recommend restaurants without knowing where you'll be. For North Carolina I suggest you spend some time on the website of "Our State" magazine. Here is a link: Our State Magazine
. Many of the best eating places are obscure local establishments sometimes highlighted in "Our State".
There is much information on the site about places to visit, events happening around the state, and good dining places. Usually their restaurant reviews are accurate, look under the "Food" tab. Under the travel tab check out the "Dates and Events" tab which will show some of the big arts festivals and cultural events going on around the state. Also under the travel tab you can click on a region (say "mountains") and be presented with a list of attractions, scenic drives, historical or cultural site, etc. you might not see on your own.
In Asheville there are many great restaurants. Check on TripAdivsor.com and read reviews of the top 10-20 restaurants. If you are in the Blowing Rock/Boone area we enjoyed a terrific meal at Bistro Roca. We also like the Storie Street Grille in Blowing Rock and often have lunch or dinner there when taking day trips on the Parkway. Blowing Rock is a delightful town to visit and walk the street. It is just off the Blue Ridge Parkway (milepost 292). The Julian Price NPS campground (milepost 297) is close to Blowing Rock.
In Asheville there is much to see and do. We highly recommend riding the trolley around town, leaving from the Asheville visitor center (36 Montford Ave at I-240; free parking). You buy a two day pass ($24 for adults, there is a $2 senior or AAA discount) that lets you get on and off at your leisure. Time your trolley trip to have lunch on the Sunset Terrace at the Grove Park Inn (warning, the Grove Park is a resort so the food is pricey). If it is a nice day, the view is gorgeous. If the food prices are above your budget, stop a the Grove Park anyway and explore the historic inn and grounds as well as the Grovewood Gallery, Grovewood Studios, and NC Homespun museum all located adjacent to the Grove Park Inn grounds. There is also an antique car museum.
Biltmore Estate is a must see in Asheville. While there, walk through charming Biltmore Village to see the shops and art galleries. There are also some excellent art galleries in the downtown area. The gardens are blooming now and should still be beautiful for the next couple of weeks. If you are a fan of the PBS series Downton Abbey, there is a special exhibition at Biltmore called "Dressing Downton" displaying 45 costumes from the series. The exhibit is included in the admission price.
Here is a link to the Asheville events calendar so you can see what is happening in the area when you are visiting: Asheville Event and Festival Calendar | Asheville, NC's Official Tourism Web Site
. Whether it be music, art, drama, street fairs, or special museum exhibitions, there is always something going on in Asheville and the surrounding area.
Don't miss the Folk Art Center on the Blue Ridge Parkway (milepost 382) near Asheville. They have a parking lot for RV's. The center has beautiful arts and crafts of high quality and is operated by the Southern Highlands Guild. I also highly recommend the crafts center at the Moses Cone Park (milepost 294) along the Parkway. Moses Cone is also near Blowing Rock and Julian Price campground. Parking at Moses Cone may be a problem with your Airstream. It would be best to spend a night at Julian Price, or somewhere in the Blowing Rock area, to use as a base to explore Blowing Rock, Boone, and Moses Cone in your tow vehicle without the trailer attached.
Should you venture east on the I40 corridor, Old Salem (historic colonial era town similar to colonial Williamsburg on a smaller scale) and Reynolda House Museum (home of RJ Reynolds and now an American art museum) in Winston-Salem are worth a visit. If you like contemporary art, the Southeastern Center for Contemporary Art is close to Reynolda House. Should you visit Reynolda House, have lunch or dinner at the Village Tavern in Reynolda Village next door. For camping near Winston-Salem I recommend Tanglewood Park, a county park about 15 miles west of downtown off I-40 before you get to Clemmons. Tanglewood has full hookup sites. Caution, some of the sites are not level.
If you go further east on I-40 to the Raleigh/Durham/Chapel Hill area there is much to see and do, plus many fine restaurants. For convenience (not scenery) stay at the campground at the State Fairgrounds in Raleigh. Further out are the state recreation area campgrounds on Jordan Lake.
Enjoy your trip.