God bless you, there IS no "real" USA. Or at least there's no one area that strikes me as more real than any other. SURreal, perhaps. Still, I think I get your meaning. For what it's worth, I'll pontificate briefly.
In the northeast, I'd make a point of going down through Philly and then south to Delaware (love the Hagley and Winterthur museums and surrounding parks), ending up in D.C. by hook or by crook. I love that whole part of the world. Perhaps spend more time in Virginia. It's historical U.S., to me, but I'm sure there's a lot of current, real stuff there as well.
I've enjoyed traveling through Kentucky and Tennessee, but I don't know that most of it would be "must see" territory, but there's a lot more reality there to be witnessed, for good or ill. If you do hit Memphis, be sure to go to Graceland, home of the King. There are many truths about the U.S. to be discovered there.
Looking at your existing itinerary, you appear to be flying and traveling by train over some of the most real portions of the country, or at least some portions I'm very familiar with. I live in Colorado, and for what it's worth, there's a lot to be seen and done in the Rocky Mountain West, and if you decide not to whip on by us, shoot me a line and I'd love to give you some ideas.
It must be said that traveling by train in the U.S. these days puts the "sur" in surreal. THAT will be an experience all its own. One bit of advice - bring food.
It's taken me too long to write this, and I now see that there are a lot of better suggestions than I could provide, but one thing mentioned really rings true - the U.S. is a big place. Heck, Colorado is larger in area than the U.K. I've vacationed all over the country (and obviously so have many on this board!), and found interesting places and people just about everywhere. I envy you your travels, and hope that someday I'll have a chance to experience your homeland as well.