Wow. The U.S. is such a big country with just about every climate, and every type of living area - rural to urban, that's it's tough to pin down just a few.
For partying and clubbing: NYC, Seattle, Portland, OR, and South Beach.
A little funky, but still touristy and/or interesting: Key West.
Gotta absolutely see one of our theme parks? Then depending on where you go: Disney World in FL or Disney Land in CA.
Everyone's raving about: Austin, TX
Eating your way across the country? NYC, Portland, OR, Los Angeles, are the biggies, but don't ignore Denver, Boston, Charlotte, NC, and South Beach.
Pure beauty: Both coasts, the Arizona and NM deserts, a helicopter ride over the Grand Canyon, the rain forests in the Great North West.
Offbeat weird stuff: google "Roadside Attractions in the U.S."
The WigWam Motel on Rt. 66 in AZ.
An airboat ride in the FL Everglades or in a Louisiana Swamp.
Gatorland - also in FL
If you like museums and/or history: Washington, DC where a lot is free because it's federally funded. NYC also for museums, art galleries, and shows (but not a lot free).
Party 'til you puke, tons of music, lots of historic things, great cemeteries, and some pretty good food: New Orleans.
It's such a big country that it's hard to land anywhere and not find something interesting, beautiful, inspiring, or delicious.
"Right is right, even if no one is doing it; wrong is wrong, even if everyone is doing it." - St. Augustine