Interestingly due to time dilation with relativistic travel you could travel almost anywhere in the galaxy in your lifetime. This is assuming you can maintain a 1-g thrust for the entire journey bringing you right up to the speed of light.

In reality there is no meaningful way to do this given the amount of energy required, and the radiation impact at those speeds. From Earth's frame of reference a ship like this travelling to VEGA will take 27 years to get there, but from the ship's frame of reference it would only take about 7 years.

Reference: https://math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html