>>The faster you go the more time slows down for you

Trivia: GPS satellites experience time dilation (relative to a stationary point on the planet) of about 38 microseconds per 24 hours - and need to be corrected on a regular basis.

If you think about the planet in 2D (so a record platter) and think about relative speeds as you move out from the spindle, the equator is experiencing time dilation relative to the poles. :-)

Also: a Bussard ramjet has a problem when it comes time to decelerate.