If you want to see the real America that made this country what it was until about 25 years ago ( when in fact it was a great nation) then forget either coast and forget all the big cities and go to the north end of route 66 and start driving. Look route 66 up on the internet and you will understand.
The "real" America does not exist, just like the "real" Europe or "real" Africa don't exist. Every single state in the US has something special and different to offer. Some places I have been and particularly like.... the Florida Keys, Maine (Mount Desert Island), San Francisco, New Mexico (Taos), and Charleston (SC). In fact, I live in Charleston and I believe it is one of the most beautiful cities in the US. You will not get the big city experience and (at least if you stay away from some areas in North Charleston) you don't run a huge risk of ending up with a bullet in your head. Great beaches (not that I care for them), great food (and I mean really great food), great fishing (yes, I do like that), lots and lots of history (Fort Sumter, beautiful plantations etc) and in general very friendly people.