MG's advice with regards to SNP is spot on. Some fantastic hiking, but with 6 or 7 nights I would definitely consider spending some time in GW or Monongahela. I also agree with the Little Devil's Staircase recommendation. It's a great hike that sees little traffic compared to Old Rag or White Oak Canyon.
Although you won't avoid crowds, there are some good fishing oriented loops in the Big Meadows area. With a little planning you could do a couple nights that string together the Rose and Rapidan rivers, give you some miles on the AT, and allow you to see Herbert Hoover's fly fishing retreat the Rapidan Camp.
For fishing in SNP in general, the first week in Oct is normally a great time. The brookies are getting ready to spawn but aren't on their redds yet, so they go crazy for just about anything you can throw at them. The most popular streams in the park are probably the Rapidan, the Rose, and the Hughes, although brookies can be found in just about any blue line on the map. One of my personal favorites is Big Run since the hike in is a bit longer and more strenuous (well for the casual fly fisherman anyway) so it sees a bit less pressure than some of the easier to access streams like Jeremy's Run or the Hughes. You can find quite a bit of information about fishing the park online at http://www.switchfisher.com or in Harry Murray's book about fishing SNP, and if you decide to head into GW, I would be glad to point you towards some streams there.
Great time of year to be out in SNP, maybe I'll see you out on the trail.