What definition of now is used in our stellar neighbourhood? Within General Relativity the idea of simultaneity is fairly arbitrary, every coordinate system has one. Which one corresponds to my personal local sense of now appears indefinable in any objective sense. One can define something a bit like a moment in time given a time-like Killing field and a (hyper) surface orthogonal to it. But, the rub is to define the Killing field over a region of spacetime in the practical sense. Of our local stellar neighborhood - perhaps a few hundred light years in diameter - we make 3D maps saying where everything is. But where everything is at one moment of time requires the definition of one moment of time.
What definition do we use in practice for one moment of time?
Note: the motive behind my question is to find out how the failure of simultaneity interacts with our instinctive experience of time in, let's call it, a Galilean mode. Even if spacetime near the Earth is sufficiently flat to be Galilean to the accuracy of our experiments, we are still setting up a Galilean frame by some implicit means. The details of that would be an answer in the intended spirit of the question. I might need to do more research myself before anyone could answer the question in that spirit. It would definitely disappoint me to discover that no one has even considered the problem.
 A: When we report the time of an observed event outside the solar system, we generally use the time of arrival of the news (carried by light, gravitational waves, neutrinos, ...) at Earth. If we're really fussy, we report the inferred time of arrival of the news at the solar system barycenter. We can't correct accurately for distance, since we generally don't know the distance well enough.
A: Even at the galactic scale things don't move much. It's all entirely classical and there is no need to drag general relativity into it. The diameter of the Milky Way is approx. 100,000 light years but it takes almost 200 million years for a single rotation. That's a scale separation of three orders of magnitude.
The proper motion of a typical star in the night sky is 0.1 seconds of arc per year. That means most stars take on the order of 18,000 years to move by a full moon diameter. Except for a few very fast ones like Barnard's star (which is not visible to the naked eye) it's all very slow out there. There would have been very few obvious changes during the entire written history of mankind in the heavens above.
Your moment of time is here and now. You really don't have to care what happens 300 light years away "at this moment". You have no influence over it and it doesn't have any influence over you. Truthfully, relativity is the universe's way to separate concerns.
