How do you stop so you don't go whizzing past Alpha Centauri at near light speed? :)
The aliens on alpha Centauri are 12 ft tall blue hunter-gatherer humanoids. Not much of a help for your parking problems.
But for an at rest observer, your ship's mass would approach infinity as its speed approaches the speed of light. This is the reason the ship would never be observed as hitting the speed of light.
In practical terms this is also why particle accelerators can't just infinitely accelerate the particles - their apparent mass exponentially increases and so too does the amount of energy required to continue to accelerate them.
A reference frame is definitionally a point from which you would measure an "apartment mass". The rest mass isn't relevant to a reference frame where that mass isn't at rest. This is true at all scales.