Every National and State park has its own sense of beauty. I used to live near the Shenandoah National Park and used to go hiking often. The Appalachian Trail ran through it and you can back pack from GA to ME along it. Not to mention Yosemite, Yellowstone, Grand Canyon, and the Grand Tetons.
i go backpacking a lot, so try Yellowstone park. its not to crowded, and its a beautiful place to visit. The Linville Gorge is also a great place. My dad's friend went hiking on the Appalachian Trail and he said it was the best thing he ever did. hope this helps!
Glacier National Park (Montana) Yellowstone National Park (Wyoming) Zion National Park (Utah) Arches National Park (Utah) Mount Whitney (California) Yosemite National Park (California) Denali National Park (Alaska) Waimea Canyon's verdant trails (Island of Kauai, Hawaii)