I don't think touring on a carbon bike is a good idea.
Touring bikes are built to take abuse.

Get an old used Mtn bike of decent quality and put Marathon Supremes on it.
And maybe drop bars.

If you are just getting started, anywhere will do.

But there is also the Rockies, the Pacific coast, I think it's called the Nashville Trace, it's a historic route in
the South I have been wanting to ride. You could fly into Burlington Vt and ride to Portland Me or Acadia, and fly out there.
Riding around Lake Champlain is great, except for some of the highways, you want to spend as much time hugging the coast
as you can.

Do a weekend trip first, even an overnighter. It will give you a much better idea
of what's involved.