Everyone has their likes and dislikes but some of my picks would be:
Glacier National Park - quite bit like Yellowstone but worth the trip to see it too.
Brice and Zion National Parks - beautiful and not as crowded as Yellowstone.
Anywhere north of Santa Barbara along the California coast - even though I was born and raised in LA I hate what the area has become in the last 20 years and won't be going back unless it was a family emergency.
Charleston & Hilton Head, SC, Savannah, GA and I'd also throw in Saint Augustine FL too - we have made this area part of our trips down to WDW.
A bit out of the US, Vancouver, BC with a trip over to Victoria - we just got back from an Alaskan cruise with 2 days in this area and spent more time there in years past. We are really wanting to go back and spend more time there. Alaska not so much, was a "once and done" for us.
Hawaii - any island, any time!
Mary Anne, have a great time planning your next trip in this great big wonderful country of ours.