Quoted from Whysnow:
Research the national parks, pick some to hit, and plan around them.
Great advice. Also I am with the rest on Chicago (amazing food and architecture), Boston (just a badass city), and don't forget our Nation's Capital. Washington DC is great, lots of history, memorials, and Smithsonian Museums. Best of all, all that stuff is FREE. Plus the Metro (public transportation) is super convenient and affordable.
My favorite city though is my hometown of Haleiwa Hawaii, a road trip there would be difficult though.