With a ship able to accelerate at 1G continuously, you can be at the edge of the observable universe in <50 subjective years [1].
[1] https://www.reddit.com/r/dataisbeautiful/comments/s4tbry/oc_...
There is a known way to achieve 100% fuel efficiency: antimatter. By storing equal parts matter and antimatter, you can fuse them to propel your spacecraft. It's unknown wether or not this kind of engine can actually be made.
Alternatively, and even more far-fetched, you could onboard a small singularity. Dumping anything into it will result in it being turned to pure energy at 100% efficiency, through Hawking's radiations. The smallest the singularity, the fastest it radiates, meaning you can sort of control the output. You can create singularities with very large particle colliders.
With 100% fuel efficiency you can probably sustain 1G for long enough to reach the nearest stars. You would need a very large spacecraft (on the order of kilometers) for a comparatively very small payload. And it would arrive completely empty at its destination, meaning no turning back. I think I saw someone do the math, but can't find it anymore.
Anyway, there are other difficulties. Travelling at .99c means tiny space dust now becomes very dangerous. So does radiations, all made extremely energetic by the Doppler effect.
On the plus side, continous 1G means you have artifical gravity for the whole trip.
The greater barrier is that the nature of the expansion of the universe prevents any real interstellar travel that has a "destination" in mind. Of course we might have some "FTL" or "near light speed" travel in futre, but if the universe is expanding infintely from every point in space at light speed, how could we ever "catch up" to objects we see even now?
Source: https://www.reddit.com/r/askscience/comments/sr7fuo/is_there...