If you accelerate at 1g half way there, then decelerate equally fast for the second half, you can reach almost any point in the galaxy in a single human lifespan - thanks to time dilation.
I'm not sure if the CMB itself will decay fast enough with the expansion of the universe to avoid 1g eventually getting you hull eroded by positron-electron pair production from photons blueshifted above 1022 keV, but that's in the set of things you need to think about.
