Welcome to the good ole US of A!
America is really, really BIG. It's beautiful. I would suggest a different itinerary, personally. My highlights of America are:
Miami, Florida. Stay in the Youth Hostel in South Beach. Swim in the crystal blue waters. Watch the sexy people on Ocean Drive at an outdoor cafe. Enjoy the delicious spicy Latin foods.
New York City--hang out in Greenwich Village, SoHo, GREAT art museums, wonderful cuisine (though very expensive). Times Square at night.
I think the most beautiful states are probably the Florida coast line (either side, the sand on the west coast is soft and white as sugar and the water is clear turquoise blue.)
North Carolina coast line at Outer Banks is remarkable as well--beautiful deep blue water, wildlife (wild horses) and fresh air, lots of history (Pirates, Lost Colony, etc.)
Colorado and Montana are REALLY beautiful states. I have heard that Denver/Boulder areas are like heaven on earth. They look a bit like the Garden of Eden.
Southwest: Painted desert. So beautiful, surely walk the Las Vegas strip and see the free shows,
In New Mexico I highly recommend the White Sands National Park (Monument?) It's dunes of sand white as snow. Remarkable. Sedona, Arizona, the Grand Canyon, Arches National Park (?) Utah is beautiful, too.
As for California, I personally HATE Los Angeles. It's a huge, enormous area full of weirdos.
Not nice weirdos like me--drug addict, hookers, con artists, etc. Hollywood Boulevard, Mann's Chinese Theatre, the Ripley's Believe it or Not Museum are fun. I highly recommend the Ivy in Beverly Hills (very expensive, many stars and celebrities of all stripes go there.) Go to Rodeo Drive in Bev Hills but just to window shop and see the celebs. I also really like Venice Beach for the freak show and fun, and Melrose boutiques for buying cool clothes and stuff.
If you want to see natural beauty in Californa, I highly recommend driving up the coast line to Big Sur and Santa Cruz area. There is a world famous aquarium up there called the Monterey Aquarium. And San Francisco is also a premier US city with all kinds of international people and great food, great things to see (Ride the cable car and the world's most zig zagging street.).
I also am very partial to Oregon and Washington state. Seattle is so amazingly fun! Exciting place and lots of natural beauty--pine forests and Sequoia trees.
Also, I do NOT recommend Amtrak. They are HORRIBLE. Just Google search Amtrak reviews bad customer service and see what kind of letters come up. They have been bailed out again and again by our government because the union is so strong that the employees are incredibly RUDE to customers!
(I took a train ride from New Orleans, LA to DC and it was the ride from HELL. Surly employees, dirty, cramped sleeping car, etc. NOT worth the almost $1,000 us!)
If I were you I would rent a car with unlimited miles (mid to full size car) so that you can pull over whenever you see something interesting and stretch your legs. To my knowledge, in America, the Greyhound buses are usually used by 'lower income' people which may not be safe to sleep...don't know for sure. Look up reviews.
Oh yes, one more possibility I've heard of is hippie bus called The Green Turtle. Google it, it's a cross country sleeping bus with friendly people. I had one friend who did it and said it was super fun.
Enjoy America!