This is going to be a little bit of a quick discussion. I was trying to travel through the US recently and found it to be quite difficult. It’s a huge country, so if you want to see multiple parts of the country, it will require a bit of planning. You pretty much have just a few options. you can fly, drive, or go by train or bus. If you go by bus, conditions will be rough and you will probably not really enjoy yourself. If you want to go by train, you might not be able to or at the very least it won’t be easy to go directly to where you want to go. The train system in the US is pretty awful. They are costly, not very fast, and inefficient. There is no such thing as a high speed rail system in the states. It’s pretty much a low speed rail system instead.
I would recommend driving across the country. The highway system is actually pretty good in the US. You will get to see parts of the country that you never knew actually existed. It will be a good time. If you go to California, driving down Highway 1 is an extremely nice looking set of views. It doesn’t get much prettier than that.