"Time travel" is real, but the only thing you can do is slow down relative to others. The way you describe is a valid method, though some might quibble that it's the accelerations involved that slow down time for you, rather than simply the movement at a high velocity.

You can also "time travel" by moving to an area of higher gravity (per general relativity). Time travels more slowly for you there, so you can let your original location get ahead of you, then go back there to effectively travel to "the future".

Of course, gravitational time dilation is a tiny effect, so you'd have to get near something unhealthy like a black hole to notice much difference.