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.

Obviously just don’t forget aiming for where we see it now is not where it is and not where it will be in 100 years.

I have never seen anyone writing about us having solid reference points to travel that far in case we can reach those speeds.

If you miss you end up in some empty space you won’t be able to mine anything for fuel to have more shots.

Just remember to account for blue-shifted CMB.

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.

Is it possible to take enough fuel and mass with you to accelerate that long without turning into a black hole?