I wouldn't go to Texas. If you want glorious landscapes, try the various mountain parks in California. California Redwoods are absolutely spectacular, and the Calif state and national parks are outstanding if you want to go camping or whatever. Crater lake, Sierra Nevadas, Tahoe, etc.
Here's a website with a bunch of suggestions in California:
http://www.destination360.com/north-america/us/california/northern-california.phpIf you want to see cities, just pick one. New York is an obvious choice but San Diego, San Francisco, and any number of others would be just as fun.
Washington DC is a nice place to visit, but stay in the tourist or otherwise public areas because although it's our nation's capitol, there is a lot of crime in many parts because the place is guverned by people who care about nothing but getting re-elected, and the people of DC are not the ones who vote for them.
The Grand Canyon is awesome.
The ski resort areas in Colorado don't have much if any snow right now, but the area is beautiful in summer and there are lots of things to do during the off-season. Hiking, camping, biking, etc. and lodging rates are often pretty good when there isn't any snow.
Mt Rushmore is sort of neat, but there isn't anything else around there so it's sort of a day-trip at most I think.
Lava beds national park is neat too. Lots of caves.
For history about native americans, the entire southwest has lots of parks and ruins. Mesa Verde is one of the best known.
http://www.nps.gov/meve/The water on the west coast is typically cold, but it warms up enough by July that the ocean in Southern Calif is swimmable. If you want to do any snorkeling or diving however, you're probably best off going to south Florida or the Florida Keys. If you have the money, Hawaii is extremely beautiful. Go to Oahu if you want shopping and touristy city life, go to Maui for less expensive fun, go to Kauai for a more nature-oriented trip.
