I would think that all psychiatric hospitals have therapy. Mine did. I don't why they shouldn't when their main goal is to help the patient feel better.

I've been through music and art therapy while staying at St. Luke's in Pheonix.

As of a patient checking themself in, I don't know the answer to that.
Most I've seen were accompanied by a family member, but the case being that most of the patients were either my age or younger. Then again, I wasn't really paying attention to all that was going on around me.

EDIT: Oh, I forgot to mention that we also did group therapy sessions as well. The boys would be separated from the girls at different times. Us "girls" would be all together working on an activity that helped us learn about coping strategies and how to build up self esteem.

This doesn't really work out for the majority of the time. We'll just go back out into the world to either move on, or, continue to carry on with our habits.