Like a few PP's, I prefer the smaller, less touristy places.
Raleigh, NC - I studied here for a semester and have been back twice. It kind of reminds me of Adelaide (in terms of the size of downtown) but waaaaay cooler. It's absolutely beautiful in the fall. The Amtrak ride from Greensboro to Raleigh was one of the highlights of my last trip. I'd love to go to Charlotte in future.
Nashville, TN - I've been there twice now, once in the fall (also absolutely beautiful) and then in summer for CMA Fest (a huge country music festival held at a football stadium). Both times I stayed near Vanderbilt rather than downtown and had no problems using the bus to get around or even walking. Highlights include Pancake Pantry, the Bluebird Cafe, the Ryman, the Country Music Hall of Fame and the State Museum. I haven't yet made it to the Opry, the Hermitage or the Belle Meade Plantation but they are on my list for future visits.
Atlanta, GA - I've also been there twice, both times I stayed with a friend out in the burbs rather than downtown. I loved the World of Coke museum and Stone Mountain. I loved staying in Douglasville with my friend because I like being able to live like an American. Plus, all the Targets are out in the burbs! I'd also love to do a roadtrip around Atlanta, Savannah, Charleston and Myrtle Beach etc.
Phoenix, AZ - I visited in November for Thanksgiving and the weather was perfect. I don't think I would brave it in the summer! We went to Old Town Scottsdale for a day which was really fun, lots of shopping and good food.
Washington, DC - I love museums
Pittsburgh, PA - Again I stayed with a friend out in the burbs, we went to a concert at Heinz Field, the Heinz museum and took a cable car up a mountain... there looks to be a few of these and I can't remember which one it was!
Chadd's Ford, PA - We drove through here just to visit the Andrew Wyeth museum, which was in a gorgeous old building, and discovered an amazing diner with a million different kinds of pie. I think we tried sweet potato, pecan and cherry and all were delicious. I wish dessert pies were more popular here in Australia!
Stockbridge and Pittsfield, MA - We stayed in Pittsfield to go skiing at Jiminy Peak over Christmas. Stockbridge has the Norman Rockwell museum which I definitely recommend, even if you're not that into art.
Sacramento, CA - I think I'm just biased because of my family friends who live here but Sacramento is probably my favourite place in the US. I'd moved there in an instant and spend way too much time looking at real estate there. It has great restaurants, a cool new artist development and is a good base for day trips.
A few other places I'd really like to go to are both Portlands, New Orleans, Houston and San Antonio, Chicago, Providence, Salt Lake City and San Diego. To be perfectly honest though, my travel (and life) goal is to visit every state haha.
Places I don't need to go to again include Vegas (not my scene at all), Memphis (I've been to Graceland and I'm not sure there's much else I need to see there) and Boston (I enjoyed my time there but not sure there's anything else to go back for).