Over generations, the night sky would more likely change from the effects of precession or even interstellar events like supernovas than from the galactic year. On the surface, this may sound odd. Why shouldn't the view change? Technically, it might, but consider a few things:
First, a galactic year in the Milky Way is nearly a quarter billion years. Divide the 360 degrees of a circle by a quarter billion and you will find that each year, we make almost immeasurable progress orbiting the galactic core.
Secondly, the core is shrouded in thick gas clouds that hide even the supergiant stars orbiting our own galactic black hole, so our view of it would not change much anyway.
Thirdly, we are in a minor spur called the "Orion Spur" (sometimes "Orion Arm") , and not very close to the core. That is a good thing, though, since we avoid some of the greater radiation and other dangers from being in a denser region. Indeed, I have seen research suggesting our solar system is more isolated than most because it was born from a hypernova explosion billions of years ago. Such explosions are strong enough to exterminate all life in a at least a quarter of a galaxy. The shock wave pushed gases outward, compressing them into our star and the solar system that followed.
I am more excited by the changes in our own solar system, which are more easily observed in a human lifetime. For example, consider the discovery of salt water beneath the surface of Enceladus or the brand new revelation of massive methane gasses each spring on Mars. The Great Red Spot is fading, but there's a giant, rotating hexagon over Saturn's north pole.
For some exciting views of other galaxies instead, visit GalaxyZoo.Org, which invites anyone and everyone to classify galaxies just discovered by our telescopes. In some cases, you may be the first human ever to lay eyes on them. Most are boring blobs, but I sometimes witness gravity lensing, galaxies colliding or being torn to pieces, and other amazing sights.