Like RAT, I've been very fortunate to be able to travel all over this country. Been to all states except Alaska, and it is definitely on the list! I spent three of the best weeks of my life last summer island hopping with the wife in Hawaii. Being able to hike over lava fields to see an erupting volcano was one of the most incredible sites. The next day spent hiking in the rain forest. Taking a day off at the beach. Then scuba diving the next... It just had the best of so many worlds.
However, on the mainland, you've got to give yourself some time and just go from National Park to National Park in the West. It's simply amazing! Although large, this is a possible feat, get in the Grand Canyon, Bryce canyon, Yosemite, Zion, Sequoia, Yellowstone (although overcrowded). They're all unique and incredible. If for some reason you find yourself in the East, be sure to get over to Acadia.