I will be homeless from May 31st to September 1st. How should I kill the time?

My roommate is bailing to Santa Cruz on May 16th so I will have to move out on the 31st. And my new apartment won’t be ready until the first of September (Lease is already signed). So I am thinking of dorking around America for three months.

Amtrak has a sort of Eurorail type deal. I was thinking of getting two of the 45 day passes and just floating around for a bit. The plan would be to mostly sleep on the train. I did it for a month in Europe and it didn’t bother me.

I also have places to crash along the way and would get a hotel a few nights a week to shower and relax.

I guess my question is where would you visit if you were me?