I love your question! Also love the idea of visiting rather than living there for life.
My first thought was to do the Oregon Trail, because it has fascinated me since childhood. But now that I've gotten old and lazy, I'd rather live in the late 1800s, in Philadelphia or Detroit. I love the architecture, furniture and styles of that time, am also interested in the intellectual discoveries happening then.
My other favorite era is the time of Elizabeth I of England. But I'd only want to visit if I could be minor nobility and go to court now and then.
Ancient Greece would also be a top choice of mine to visit, back when the Parthenon was still in one piece.