Someone emailed asked me about campgrounds with showers, so thought I'd post.
The Parkway has campgrounds every 75-100 miles or so. I know they were planning to put showers in some, I don't know if they are completed. You could contact the Parkway by phone (don't rely on internet) to find out.
If you are starting in VA:
At about MP (milepost) 18, near Love, VA, is a Forest Service campground called Sherando Lake. They have lovely campsites, great shower houses, a lake etc. It's not as cool as higher up the mt, but very very nice.
If you don't mind a somewhat longer excursion off the parkway in VA you could check out Fairystone State Park. I think they have showers, but you'd have to check.
Around MP 165 is Rocky Knob campground. It's high on the mt and just altogether lovely. You can pay an extra 2.50 to take a shower at the Rocky Knob Cabins. They give you towels and soap, which is nice, so you don't have to worry about carrying wet towels. And the campground is SO lovely that it's worth the arrangment.
(The cabins themselves are wonderful, so think about staying there if you just need a night out of the weather or a bed. They are CCC era, some with stone fireplaces, all with porches and rockers. There's a nice hike near them, too.)
(And then, get a meal at Mabry Mill Restaurant. They serve breakfast all day, and are famous for buckwheat pancakes and peach cobbler.)
Very near Mabry Mill, at Meadows of Dan, is Willville (not a town but name of motorcylce campground), which has showers, coffee, brreakfast bisquits. It doesn't have the views or same loveliness as the Parkway, but it's nice and the owner is great. (Tell him Ranger Love sent you.)
You'll find several private campgrounds in the Boone/Blowing Rock area. I seem to recall staying at Bear's Den and some others with my kids. If you stay in that area, it's fun to go into Blowing Rock for a little shopping and/or ice cream. There's also some nice hike to a waterfall near there, but can't quite remember where--ask a ranger in that area. .
There's a campground near Linville Falls that has showers and a tent area but I've never stayed thre. check
www.linvillefalls.comNear the Spruce Pine/Little Switzerland part of the Parkway, there's a US Forest Service campground that had showers. The down side is it's further down the mt, which means hotter, buggy (I never encountered mosquitos in Parkway campgrounds), and at least when I was there, more crowded. Maybe they'd let you come in just for a shower (I think they do that).
See if you can get the Forest Service's publication (maybe online?) that shows their forests in Va and NC (Nantahala, Pisgah, others) and check the campground info.
There are several campgrounds near Asheville. Look up Beark Creek at
www.ashevillebearcreek.com,
www.campfirelodgings.com (it has yurts), and wwwashevilleeastkoa.com
Around MP 443 is Moonshine Creek Campground, never stayed but it says hot showers. www.moonshinecreekcampground.com
Maggie Valley, which is near the Smokies, has a gazillion places to stay and a cool town (not Parkway) visitor center that goes to extraordinary lengths to help you find something. (I was directed to a camping cabin somewhere during a terrible rain, and it was wonderful.) Checkwww.visitmaggie.com
There are other private campgrounds all along the Parkway and most if not all would have showers. I also suggest getting info on cabins (or campgrounds with camping cabins) for those miserable rainy nights (in some years, the hurricanes and tropical storms go straight up the Parkway.) BTW Willville has one camping cabin, with double bed, but it gets reserved quickly.
Campgrounds often advertise in the Blue Ridge Parkway Directory and Travel Planner, put out by the BRP Association. If you don't have time before your trip to get one, it's given away for free at each visitor center. It also has great info on where to get gas, attractions, flowers you'll see, etc. and is arranged by milepost, so when traveling, and you think you might stop in an hour or two (which means 45-90 miles, since you are doing the speed limit), you can look ahead in the booklet to see what's available.
Be sure to bring warm stuff. It's been in the 40's at night in August up there. (It will be colder on the Parkway than private campgrounds, because in general the Parkway follows the top of the mts and everything else is lower.)
The visitor centers on the Parkway would also have more info, including brochures, on area things, but they don't put the brochures out because people end up trashing the centers with them, so you have to ask for them. (Rocky Knob keeps a notebook with brochures in plastic page protectors, by milepost but that's just for that area)
BTW you should check out Floydfest if you are going in July. Not sure of the date of it this year.
Drive safely and have fun!