I have been in all the states in the U.S. However, as a truck driver, there were a lot of places I couldn't visit.
Much of the U.S. is never seen by those from outside our country. The reason is easy. The U.S. is huge, and traveling is not as easy as in Europe or the UK, where you can hop a train to anywhere.
The Grand Canyon is great, and it's in an area that is very much unlike what most of us think of as Arizona. That is, it's at over 7,000 feet altitude, it's cool in the summer, with pine trees, etc. A night at the El Tovar Inn (look it up--it's an old Harvey House, right on the rim) is worth the expense.
After that, I'd love to have you see Yellowstone National Park. You probably can't get a room at the Old Faithful Inn, but be sure to at least go inside.
To really see America, you should drive from New York to Los Angeles, taking I-80 to I-57 (Chicago) to I-55 (with a stop in Memphis, for Beale Street! I have a musician friend who could take you out for great music, great ribs, and maybe a visit to the Gibson Guitar factory), to I-40 (Little Rock) to I-30 (Dallas) to I-20 to I-10 across Texas to El Paso, across New Mexico, Arizona (Tucson and Phoenix) and all the way to Los Angeles. Drive back by going up I-15 to Las Vegas all the way up to Salt Lake City. Continue on up to I-90 and go across Montana (follow the Yellowstone and Missouri Rivers), South Dakota (stop at Mount Rushmore), Minnesota, Wisconsin, and back to Chicago.
That shouldn't take more than about 3 months!
And even then, you'd be missing going across I-70 from I-15, seeing some of the most beautiful country in the West and some of the most productive land in the Midwest.
And then, take a flight to Seattle and eat at Ivar's Acres of Clams! Just as an example, there are about 15 different salmon dishes on the menu.Ivar's Dinner Menu