Oh we
know time slows down at high speed. Its been measured. Einstein figured it out with a piece of chalk, but eventually we were able to actually verify it. We've also measured relativistic effects in spaceflight. The ISS for example actually passes time slower than the earth, which sounds backwards until you consider that its zooming around in a big nasty gravity well. Gravity speeds up time, velocity slows it down. Satellites have to be programmed to account for relativistic effects. Etc etc etc.
Traveling faster than light is supposed to be impossible. There's quantum tunneling...and those guys from Cern who thought they sent neutrinos from place to place faster than light...but zombie Einstein bitch slapped them and they stfu.
If you were to actually travel at the speed of light...you'd have infinite energy and infinite mass and would exist simultaneously everywhere in the universe. God essentially. Good enough. Time travel. Sure why not.
Actually exceeding the speed of light though....uhhh...pretty sure that would break the internet.
I'd go to some future time and hope they've invented immortality. Then after that I'd be a tourist.