IIRC, it is possible to get anywhere in the observable universe in one human lifetime assuming 1g of constant acceleration.
This does not permit you to slow down and halt at your target, which greatly increases travel times.
It is also effectively a one-way ticket for anything other than objects in our immediate stellar neighborhood. If you turned around and returned to Earth after getting to an object 1,000ly away—still well within our own arm of the galaxy—at least 2,000 years will have passed on Earth. It’s probable that no civilization you know of would still exist, nor would anyone be able to understand your language.
This isn’t even beginning to address the problem of running into stray atoms at 99.99…% of the speed of light. Or god forbid a handful of stray molecules. We also haven’t discussed the real elephant in the room which is the sheer amount of energy required to accelerate a human and human life support systems at 1g for several decades.