Allan, it is true that you’ll need almost infinite energy to get near the speed of light (if you are a material object the size of a human being), but taking aside this and other technical limitations, there’s nothing in Special Relativity setting in stone the amount of time you’ll feel while traversing the universe almost at the speed of light.
if you are allowed to get arbitrarily close to the speed of light, it could take you 56 years, or any other arbitrary amount of time.
If 99% the speed of light makes your trip take 56 years, then just accelerate to 99.99%, or 99.99999%, or as close as you need to get the time elapsed you want (it will take you that time in your subjective experience. All the aging effects Jonmaas describes for the rest of the universe will take place as described).
But now, switch to the point of view of something really going exactly at the speed of light. What do massless quanta feel?
By going exactly at the speed of light, photons and other massless particles feel they traverse the universe IN NO TIME (for themselves). They feel leaving and arriving at the same time. So they don’t know our space or time dimensions exist (!)
They feel all the interval we observed as compressed into a single “flash” of existence. Photons and massless gauge bosons feel they are INSTANTANEOUS. I repeat: from their own point of view, they are instantaneous connections, they are like wormholes connecting different spacetime coordinates in no time.
This dual perspective (that any PROCESS that we observe as developing at the speed of light is, at the same time, an instantaneous point-like EVENT from the perspective of the massless quanta that comprise that process) explains a lot of the weird stuff that plagues Quantum Mechanics (entanglement, nondeterminism, wave/particle duality, wave function collapse, Bell’s theorem, faster than light communication, EPR paradox, Scrhödinger’s cat experiment, double-slit experiment, delayed choice experiment…)
You can look at all these topics in more detail here:
