I would do several things. I would go back to Vienna circa 1910. I would find Hitler, who basically spent his time wandering the city doing nothing during that time period (this was before he went into politics), and kill him.

Being a pianist and composer, I would also go back and see Mozart, Beethoven, Chopin, Liszt etc. As someone who loves their music so much, it's hard to imagine anything more thrilling. We really don't know how they actually played and conducted their compositions, given that they lived before the phonograph was invented.

If I was going back to 1955, the year they travel back to in the first "Back to the Future," I would visit Albert Woolson. Woolson served in a Union regiment from Minnesota during the Civil War. By 1955, he was the only known survivor of the war from either side. As a Civil War buff, one of the things I regret is not having lived when there were still veterans of the war around to talk to.