You're correct, Smoke, the US Army Corps of Engineers designed/built/operates many flood control and water supply projects (dams and reservoirs) in the middle and eastern parts of the country. Similarly, the Tennessee Valley Authority and even some for-profit electric utilities. Many if not most all COE and TVA lakes have camping facilities and most are pretty nice. Every COE facility I am aware of offers advanced booking via the Federal NP, NF, NM, BLM etc online reservation system at www.recreation.gov. Pretty much any large reservoir in WV, KY, VA, NC, and TN is likely to be a COE, TVA, or public electric utility lake with camping readily available. There are some interesting "paddle-in" camping opportunities at some.
Even though I shy away from the crowds on the BRP in October, I will here suggest consideration of booking a mid-week campsite at Julian Price Memorial Park, a NPS campground along the BRP just south of Blowing Rock and in the shadow of Grandfather Mountain State Park. Price Park Campground has two loops and one of them is on 45 acre Price Lake. The campground on the whole is on a trail network including parts of NC's Mountains to Sea Trail (MST), with connections to the Tanawa Trail (a BRP trail system), to Moses Cone Memorial Park (another BRP unit, but sans campgrounds), and the Grandfather Mountain State Park backcountry trail system (pack-in camping by permit only). Price Park and Cone Park are NPS properties on both sides of the narrow BRP corridor which were donated to the NPS in the 20th century by wealthy families which had strong ties to the NC Blue Ridge Mountains. Price Park is around 2,500 acres and Cone Park is nearly 3,000 acres--both are mostly back country and Cone Park has +25 miles of gentle grade carriage trails looping through it. Price and Cone parks are contiguous and Price is contiguous to Grandfather Mountain SP on the other side. So, with GF Mtn's 2,600 acres of back country, we have about 8,000 acres of densely forested back country with good access via trails, most of which are foot trails only (Cone Park being the exception, allowing equestrian access, which is well used during Spring-Summer-Fall weekends.)
Less than 40 (slow, twisty, slow, and twisty) miles from Price/Cone/GF Mtn is Grayson Highlands SP in Virginia. It's adjacent to the Jefferson NF as well as segments of the Appalachian Trail (AT). The areas around Erwin, TN and Hot Springs, NC are in AT territory, too.
Both the NC and the VA state parks systems offer online reservation booking. In the case of Price Park, above, be aware of the 6 month rolling window for reservations via www.recreation.gov. I understand the Price Park campgrounds spots get booked up exactly 6 months to the day before Fall weekend dates, so be aware as March and April arrive.
I'll offer up some specific hiking ideas a little later.
Foy