Ok, nobody else has offered this basic fact you need to address with your trip planning: the US has no real public transport infrastructure.

I assume from your sentence structure and word choice - and that you are "visiting the US" - that you are not American. Probably European.

Anyway, you have never been somewhere as big as America with as much space between things. Unless you have spent an unreasonable amount of time in the Taiga or the Australian Outback, there just aren't parts of world as spread out and inaccessible as America.

So you need to get from one place to another? We fly or we drive. Period.

My friend just drove from Seattle to North Dakota and back to buy a cat. That's three times the distance from London to Edinburgh... one way.

This is the thing that foreigners just don't get about America. It is goddamn huge, and we hate tourists who don't rent cars.

I think you'd be much better off flying between four different "hub" cities, and once in those cities, use local service like Uber, and CouchSurfing to find ways to get in, out, and around town.

New York. Seattle (or Portland). New Orleans. Atlanta/Memphis/Charlotte.

These cities each embody a different part of what America is, they have rich infrastructure to support exploration, culture, meeting people, etc, and they also are nearby to amazing things you can go do "out of town" for an afternoon or a weekend. Hiking. Sightseeing. Museums. Cultural shit.

With Couchsurfing or AirBnB "shared room" accommodations, you also get to meet the hosts, who are excited to have you in town, show you around, and connect you up with their fun friends who are going camping this weekend, or have a boat, or maybe are playing in a band at show at a local club.

THAT is going to give you way more of an "America" experience than sitting on shitty, piss-smelling buses full of ex-convicts for 2.5 days, or getting dropped off in the ass-end of town by Amtrak, 15 hours late, in an unsafe area, with no transport options into town.

There are also a lot of people who are driving somewhere far away, and don't want to do it alone. So they post on Craigslist, or other sites, and are looking for someone to pitch in some gas money, good tunes, and conversation to make the hours on the road pass by faster. And there are heavily traveled corridors (like Interstate 5 between Seattle and LA) where you could get a ride probably any day of the week.

So I'd rethink your itinerary. What do you want to learn about America? Do you like people? Do you make friends?

When I travel, I prefer to find a place to stay, and stay there. Buy groceries from the local store. Make my own food. Meet people at the local bar, etc. I don't want to touch the "tourist" areas of any city. Take me to a dive bar instead, and let me talk with real people. Not people who are paid to smile at me and pretend they give a shit...

So... yeah. That's my list of suggestions...