The Universe Within 12.5 Light Years

For getting the feel of the milky way, I think there's nothing that is better able to simulate it than a video game, ala Elite Dangerous. I loved to navigate its galaxy map. The size of the Milky Way, the numbers of stars and distances between them are of scale in there if I recall correctly.

Unsurprisingly with ~400 billion star systems, less than 0.01% have been explored.

If there were galactic empires like you see in science fiction, the amount of administration required to deal with that many systems would be mind boggling, the volumes of data would be staggering.

In the Foundation series the old empire's central planet Trantor was just one giant city that did almost nothing but administrate the empire.