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.

I am not familiar, so I don't know, but do they assume something like 31,536,000x speed of light to make the galaxy even remotely navigable, e.g., the ability to navigate from Earth to Alpha Centauri within 4.34 seconds?

There's FTL travel of course, but you can navigate at 'normal' speeds as well. The normal speeds really show how there's no way to get to any other object even at full throttle (without FTL). It's just for asteroid belts, space stations and so on. the way they did it gives a really nice intuition of the enormous size of space. It's a fantastic game!

I suppose they can’t simulate time dilation, which does make it possible to visit other galaxies without FTL.

You certainly could simulate time dilation, I'd be surprised if that isn't already an element of some game out there.

If you go close enough to the speed of light, what you actually see is that space appears to shrink (in the direction of travel) and the trip seems to take less time than light would, because you've apparently covered less distance. Of course what those on the planets would see is that time has been moving oh so slowly on your otherwise speedy ship. There are equations you incorporate into a simulation that would account for this. If the game mechanics were such that you could could see what day/month/year it is in local time, vs your ships time, it would quickly become apparent that bashing through the void is no way to get anywhere.

You couldn’t simulate time dilation in a multi player game, at least not in any way that didn’t involve some players waiting for others.

Sure you could. Each local area (such as a planet) is a single timezone, and everyone there experiences time at the same rate. Someone leaving that timezone would experience time dilation... But in game it would just appear as a communications lag, just as it is for people on different planets. Then, once you've arrived at your destination, there's no longer any lag with your new timezone, and your lag with the original time zone is now fully synched with everyone else on your new planet.