DH and I love to travel internationally and within the US. Some of our US favorites starting from northeast and moving more or less clockwise:
(1)Northeastern states of New Hampshire, Vermont, Maine for the mountains and seashore (Maine). Especially beautiful in fall for leaf viewing.
(2) Mid-Atlantic - Philadelphia, Pennsylvania, Baltimore and the eastern shore of Maryland, Washington D.C., Williamsburg and Richmond Virginia especially if you are interested in colonial history.
(3) Southeast - Hilton Head, South Carolina and Savannah, Georgia for beautiful beaches and more history. Savannah is adorable.
(4) Great Smokey Mountains National Park in North Carolina and Tennessee. Include Asheville, North Carolina and visit the Biltmore Estate (largest private home in US). Great hiking, kayaking, water sports, beer and food.
(5) San Antonio, Texas - visit the Alamo and stay on the Riverwalk. Just beware...Texas is huge. Don't be fooled into thinking that you can just do day trips and see the whole state. You could start in Houston and do a road trip and stay a couple of days in each Dallas, Austin, San Antonio and end in El Paso.
(6) Southern California - start in San Diego at least 3 days then drive up the coast highway as far as you have time. The Hearst Mansion is impressive and his influence on American politics and history is amazing. Los Angeles is huge and crazy and has DL. San Francisco is beautiful and very different. I've heard that recently it has become seedy but have not seen it.
(7) Washington and Oregon states. See Mount St. Helens in Washington then spend a couple of days on the Oregon coast before following the Columbia River inland past magestic waterfalls. Turn south and visit Bend, Oregon and Crater Lake in Oregon. If you still have time head down to northern California and the Redwoods National Park.
I've not been to many of the national parks in the west other than the Grand Canyon. My friends have loved the trip through Wyoming, the Dakota's, Arizona, etc. so it's on my list.