So I ended up hiking down from Skyline Drive my first day and fished the Rose River a couple miles down and found it to be an absolutely beautiful stream with enough willing brookies to make me happy. The second day I did the same thing and hiked down to the Robinson River and found it to be just as nice with the added bonus of having the entire stream to myself, save for the occasional hiker. On my way back home that day I found a spot along the Shenandoah River and caught a smallie and some fat bluegill that put a good bend in my 4 weight. After the strenuous hikes back up to my truck I changed it up on my last day and drove to the lower portion of the Rapidan River and hiked up to fish for a couple miles, which was a nice change of pace. The Rapidan was beautiful and I caught some brookies, but they were definitely more spooky and harder to catch.
Thanks for all the advice and I'll definitely be back in the future...although I think you could spend a lifetime fishing that area and never fish every stream.
"I wish I was fishin'..." -me