As a historian, I'd travel into the past.
Probably the middle ages in England however, since I'd have a significantly easier time adjusting than if I were to travel further back and join a foreign culture, like the Romans or the Ancient Greeks.
Thing is, I'd mainly be doing this for the pleasure of seeing it all as it occured, but the real benefit of that would be if I could take the knowledge back with me to the present, to share, or use to make findings.
So, if I had to live back then, I'm not sure if I'd want to go.
If I did however, I'd be tempted to change human history.
And the main way I would do that, would be by creating a few basic modern inventions/practices.
Namely generating electricity (simple with a basic turbine), advancing the idea of antiseptic and asepsis in order to greatly improve healthcare, as well as a few more procedures, like basic vaccination (Edward Jenner style), pasteurisation and hopefully the discovery of Penicillin.
The printing press would also be cool to devise, but I don't really know the exact mechanics of one, but I suppose I could work it out.
I don't think I'd be able to revolutionise the world within my lifetime in the past, but I could certainly bring things about to occur earlier than they should have. And thereby allow for others to research those areas earlier, and hopefully advance to our modern state. :)
Ancient rome during Caesars rule baby
(As long as I get to be a proud citizen of rome)
Mmm, what better time to live than in the middle of a period of intense civil war! You get like 5/6 years of peace after Pompey dies until Caesar is assassinated, and then you get another 15 odd years of civil war between Octavian and Marc Antony.