I would end in Damascus. It has easy access from I-81, easy parking, and good food when you are done. Shuttle with Lone Wolf, Gypsy Dave, or Mt Rogers Outfitters.
For a starting location, I'd choose the Mt Rogers HQ building, 65 trail miles north. For a slightly shorter hike, start at the bridge over the South Fork of the Holston River, about 56 miles, or at Fox Creek, about 43 miles. All depends on how long you can or want to hike per day, and how many days.
The open high country is about a 15-20 mile stretch of this hike. You'll come up from the Fox Creek road crossing to the top of Pine Mountain, see a great view, then head back into the woods

. Then come back into the open at Scales, followed by a long traverse of Stone Mountain with great views, then past Wise Shelter (good campsites right before the shelter *before* you cross the creek into the state park), then climb to Massey Gap and back into the open up Wilburn Ridge. That's a nice climb in the open to Rhododendron Gap, then it mostly stays in the open past Thomas Knob Shelter until you get around Mt Rogers (do take the side trail to the summit, it's not open but it's pretty). You'll get a little more open area at Elk Garden, then climb Whitetop in the woods, coming out in the open for a lovely walk across the side of the mountain to Buzzard Rocks for a terrific view. Then the very long descent to US 58 and you'll be in the woods and in the creek gorge the rest of the way to Damascus. Consider taking the Virginia Creeper Trail (an old railroad bed trail) all the way to town once you cross the Hassinger Bridge at Creek Junction. It's a more pleasant walk. Or take it once you come down from Straight Mountain and the Saunders Shelter. (Also, too, you should stop at the Creeper Trail Cafe in Taylor's Valley along this stretch, they are only open 11-5 but worth the stop for a burger and some ice cream if you time it right.) There are good campsites in several places along the Creeper Trail.
Summer weather is generally pleasant, especially up high, with highs in the 80s (F) and lows most likely in the 60s but it can get chilly sometimes. You'll get afternoon thunderstorms most days, though they won't always hit right where you are. It's not like summers up north -- there's plenty of humidity and it'll be hot in comparison -- but it's much better than down in the flat lands.
My wife and I are the section editors for this stretch for the ALDHA Companion, so we're kind of partial to it.

You can PM me with any specific questions. Hope you enjoy it.