Well we used to play a more elaborate version of time machine in the history dept. grad student offices. I'll give you my top 3 destinations, and that pretty much explains how I see it. It's never about changing anything, it's about being able to experience what I missed more than anything else.
1. New York City - Greenwich Village, late 1950s-early 1960s. >> To be able to hang out in the small clubs and hear Miles, 'Trane and the rest of them play, and maybe a young Robert Zimmerman too. Perhaps the greatest collection of sheer musical talent to be pretty much all at the same place at the same time.
2. Yasgur's Farm, Bethal New York, August 15 to August 18, 1969 - because I'm a hippie that's why.
3. Rome, 64 B.C.E. to about 100 C.E. The reign of Augustus and beyond. Pretty much the height of the Empire, and I'd love to see what they really did in the Colosseum - there were never any shows produced like that before, and certainly not since.