From: Northwestern Georgia, USA
As a life-long American who loves to travel, loves history, loves nature, and writes about all of these topics, here's how I might package some 3-week vacation opporutunities:
South: Great Smoky Mountains National Park (with enough time to do some hiking to Abram's Falls and Charlie's Bunion, plus the drive through Cade's Cove); Chickamauga Battlefield; Atlanta (history and culture - sort of); Cumberland Island National Seashore; Florida (including some of the theme parks, Cape Canaveral, Miami - what a cool and beautiful city - and the Florida Keys).
Northeast: New York City, Boston, Acadia National Park in Maine, Niagara Falls, Gettysburg, Harper's Ferry, Fort Ticonderoga, and lots of time at Washington D.C.
Northwest: Yellowstone/Grand Teton, Glacier National Park, Seattle, Olympic and Cascade Mountains, Oregon coast, Crater Lake National Park.
West: Grand Canyon, Zion, Bryce Canyon, Mesa Verde, Yosemite, Redwoods, San Francisco, Pacific Coast Highway.