What shenanigans would you like to pull off if given access to a time machine? For example: Go back to ancient Egypt and dump a truckload of LSD into the Nile and see what the hell happens to human civilization. Does art take a dramatic boost? Do the pyramids get built in weird shapes? Another one: Bring back a bunch of modern animals and introduce them to an extremely ancient ecosystem and see what changes over millions of years of evolution. What goes extinct and what traits change? Give Beethoven an electric guitar and see what he comes up with. Play some LP for Mozart and see what he does with the ideas. Let's make this into a game: comment what you think the fallout would be from previous people's ideas then propose your own.
All I'd use it for is to prevent Liverpool from losing to Chelsea two sundays ago. World would be a better place.