I highly recommend getting this map:
Shenandoah National Park (National Geographic Trails Illustrated Map).
With this good map of the park, you can explore the streams.
There are so many streams to fish there. We only fished two of them, and had good brookie fishing on both. But I've heard from other people that they also had good fishing, on streams different than the ones we fished.
Are there any streams in the park without a trout population?
We just tried to pick streams that we thought might not get too much fishing pressure.