First Steps

When traveling you don't want to call attention to your self, you want to look like every one else. That means dressing and acting like everyone else. Same as a guy in a 3 piece suit at a Phish concert would stick out, having a spike Mohawk and wearing a "Fuck Trump" t-shirt will cause agents of the state to notice. It would be best to dress as drab as possible. Same as your behavior, speak to no one unless it is necessary, don't sit or stand away from people. Being in a crowd means you will not stand out.

Plan you trip well in advance. Know your route and all the stops you might have make.

Avoid any and all contact with the police, never get in their field of vision.

Plane

NO. It is not possible to travel by plane with the state noticing. Flights have to be book ahead of time on a website, either the airline or a travel site, with a credit card. That is a minimum of 2 database entries. Then one has to go through TSA screening where you have to present government issued ID. Just showing up at the airport with no baggage, waiting to buy a ticket with cash for a one way flight that day is going to set off all sorts of alarm bells. An additional problem is planes travel in well established routes. If the state finds you are on a flight and they want you they will just turn up at the gate when you land. Plane travel is off the table.

Train

NO. Amtrak requires a government issued ID to buy a ticket. You will be required to present the ID when boarding the train. Train travel is problematic in America. Outside of the Northeast corridor it runs sporadically with frequent delays. Plus the train make schedule stops. If the state wants you they lots of time to pick you up at any of the stops. Train travel is a no.

Commercial Bus

(greyhound, etc.) - no

Motorcycle

No.

Ride Share

Maybe

Car

Yes

Bicycle

Yes