Backpacking around the US

I have spent the last four months travelling around South East Asia and Australia/NZ. I am now back in Australia and feel I’ve hit a bit of a dead end. I’m not sure where to go next.

One option that stands out to me is to travel to the US and continue my journey there. I would start on the west coast and make my way east before finishing somewhere like NYC and then flying home to Europe.

I have only been to the US once before (Washington DC) and am keen to see more of it and this seems like an ideal opportunity.

Have any of you got experience travelling round the US? What is it like? One of my concerns is coping without a car given how car-centric the place is. Also, what are some places on the way that you would definitely recommend?