If you can afford the time and money, I'd say go west, young man. Others know a lot more than I do, but I'd say Rockies, Sierras or Cascades.
If you need to stay more local, for a week I'd say Adirondacks or White Mts (NH).
Adirondacks (~6 hours from Philly): for isolation, there's lots of places. For views, the High Peaks Region, but expect lots of people. Favorites: Haystack, Basin, Gothics, Giant of the valley.
White Mountains (~8 hours from Phil.) for isolation, the Cohos Trail. For spectacular views, Presidential Range(Mt. Wash., etc) and lots of lesser known peaks. Again expect lots of people.
Mt. Katahdin, Maine is a long ride, but is supposed to be spectacular.
Catskills (~4 hours from Philly). If you have a week, go to the Adirondacks, but when you have 2 or 3 days consider the Catskills. Cornell, Wittenberg, Black Dome, Blackhead are pretty nice.
If you joined the forums at http://adkhighpeaks.com/ and asked you might find people in your area to carpool who go north for weekend peak bagging or hiking.