After college I took a 9200 mile road trip in 19 days. We started in Oakland, went to LA, drove to New orleans, up to baltimore. Leaving baltimore we decided to call the Oakland A's after game radio show, and they loved that we were out on this adventure, so they had us make a big sign to bring with us to baseball games (we weren't really touring baseball parks, but had planned on stopping at any we could). Brought the sign to NY, Then boston. Then they got us free tickets to see the A's play in Kansas City, were we got to sit with the players family's who got us some autographs (tim hudson and Jason Giambi) on the sign. From there to Chicago (new comiskey, cubs weren't in town), across to seattle, and finally back home. The next day we took part in the taco eating contest on the field of the oakland coliseum.
We slept at friends houses, lots of truck stops. Did a lot of 24 hour driving. Got out stuff stolen in baltimore, didn't shower for days. By the end of it, my friend and I hated each other, which was a problem since we had gotten a place together to move into afterwards too. We worked it out eventually though.
We went hours out of way to see Mt Rushmore and the corn palace, cause, you know, when the heck am I gonna be in south dakota again.
Great trip, I totally recommend doing something like it while you are still young and don't have the responsibilities. Get a truck with a camper shell, put some pillows and blankets down in the back. Stock up with beef jerky. Always take your leftovers with you for a snack, don't go into strip clubs in new orleans during the day. Thats about all the advice I have for you.