The shenandoah streams are some of my favorites in the area period, but especially for taking friends out to try to get them into fish, so I would second Terry's recommendation on that. They won't be huge but you can generally find good pocket water to fish where they won't be too spooky and you don't need much casting skill which helps if your brother is a beginner.
Like Terry said, the water can get low during the summer, but most of the reports I have seen suggest that this season has been pretty wet compared to normal, so i think you will still do well even this late in the summer. Checking with Murray's shop is probably a good bet.
Another thing to mention about the SNP streams is many of them can be fished either from the bottom of the park boundary by driving / hiking up from various parking areas or access roads, or from the top, by hiking down from Skyline drive. Coming in from the bottom will give you more water and (in my experience) chances for slightly larger fish. But from the top you can get some nice hikes with awesome views. So you can take your pick depending on what you feel like.