Part One of Two: Natural Space Beacons.
As Douglas Adams wrote:
“Space is big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space.”
And space is also transparent. Very, very transparent. Objects billions of light years away can be detected by astronomical instruments.
The universe is full of objects in various locations which naturally transmitt at various wavelengths. If you at the night sky at a place far from light pollution you will see many such visual light sources.
So if the Galaxy Far Away is like our Milky Way Galaxy, a spaceship in interplanetary or interstellar space will not have any problem with light pollution obsuring its vew of space.
So if a starsip is within the disc of the Galaxy Far Away navigators and navigation computers should be able to see the disc as as a band of light in a circle around the ship's positon. And if that band is brighter in one direction that should be the direction to the galactic center.
And the ship's sensors should be able to pick up sources of various wavelengths of radiation, such as radio waves and X-rays and so on. On Earth, the brightest source in any wavelength is naturally the Sun. but the next brightest source in many different wavelengths is often a very distant object.
For example, the Galaxy M87 was among the first objects other than the Sun to be detected in radio wavelengths and in X-ray wavelengths, since it is one of the brightest objects in the sky in those frequencies, even though it is over fifty million light years away.
Another early detected and thus very strong radio source was Sagittarius A West, which turns out to be the center of the Milky Way Galaxy, about 26,000 light years away.
In visible radiation, here is a list of the 93 stars, including the Sun, which appear brightest as seen from Earth.
Excluding the Sun, there are two stars which are less than 10 light years from Earth, many stars which are between 10 and 100 light years from Earth, many stars between 100 and 1,000 light years from Earth, and six over 1,000 light years from Earth, including Deneb at about 2,615 light years.
So in any part of a galaxy, some of the stars which appear brightest may be too close to be good for finding your positon, and some of those stars might possibly been too far away to be good for finding your posiiton, and some of those stars should be at just the right distance for finding your posiiton.
And the same thing goes for the brightest objects in various other electromagnetic frequencies. Among bright objects observed at radio frequencies are quasars, and most quasers are billions of lightyears away.
Because quasars are extremely distant, bright, and small in apparent size, they are useful reference points in establishing a measurement grid on the sky. The International Celestial Reference System (ICRS) is based on hundreds of extra-galactic radio sources, mostly quasars, distributed around the entire sky. Because they are so distant, they are apparently stationary to our current technology, yet their positions can be measured with the utmost accuracy by very-long-baseline interferometry (VLBI). The positions of most are known to 0.001 arcsecond or better, which is orders of magnitude more precise than the best optical measurements.
External galaxies could range in distance between tens of thousands of light years and billions of light years. The brightest ones are likely to be the closest ones.
Most large galaxies contain a varying number of globular star clusters, which are as bright as many thousands of stars, and can be observed at great distances. The nearest globular clusters are thousands of light years from Earth, and the farthest in our galaxy are hundreds of thousands of light years from Earth. And there should be approximately the same range in globular cluster distances as seen from most regions of the galaxy.
Pulsars are stellar remnants which emit strong pulses of energy. The nearest few are less than a thousand light years from Earth, and the farthest should be tens and hundreds of thousands, and maybe even millions of light years, from Earth.
There are over 1,000 known open star clusters in our galaxy, and probably several times as many undiscovered ones. According to this list:
The distances to the known open star clusters in our galaxy range from 47 parsecs to 8,870 parsecs, or 153 to 28,929 light years.
So all of the different types of cosmic landmarks mentioned so far have different though overlapping ranges of distances. So if a starship mananges to identify a few dozen landmark objects, some of them should be at the right distances to identify the starship's position very accurately. Modern astronomical instruments can measure very small differences in the angles to astronomical objects.
Part Two: Artifical Space Beacons.
In various Star Wars movies and televison episodes, characters use communications systems to talk with other characters in different star systems at least a few light years away, and and possibly tens of thousands of light years away. Thus interstellar communications in Star Wars must use some sort of radiation which travels at least millions of times faster than light, and possibly is instantaneous.
If it is possible to generate such radiation artificially, there may be natural sources of that radiation, and so those natural sources may also be cosmic landmarks for interstellar navigation.
And when interstellar messages are sent using such faster than light radiation they might be broadcast in all directions, or narrowcast on a very tight beam. Possibly some times of transmissions are broadcast in very direction and some use tight beams aimed at specific locations.
Any faster than light signals which are broadcast from important planets in the Galaxy Far Away can be used to fidn the directions to those planets, and thus use those planetary broadcasts as cosmic landmarks to find the position of a starship.
And since there has been interstellar travel for many thousands of years in the Galaxy Far Away, some socities might have established artifical beacons of faster than light signals, beacons located in different regions of the galaxy, to use as navigation landmarks in space.
Such artificial faster than light beacons in space would be the equivalent of of the GPS system on Earth. And if natural objects in space are not good enough for space navigational purposes, such artifical GPS eqivalent beasons would have to be set up to keep stars from becoming lost in space.
The OP says:
Of course, the GPS system wouldn't work in space. However, instead of using satellites, one could place long-range transmitters on various planets, moons, or other predictably-moving objects. My headcanon suggests that this type of system is used in the Star Wars universe. I have come to this conclusion based on the fact that the navicomputers don't work in the Unknown Regions. The navicomputers don't work there because the Unknown Regions are out of range of any location transmitters.
And if the navicomputers don't work in the Unknown Regions because they are out of range of artifical beacons, that would mean that navicomputers don't detect the radiation from natural objects, only from navigation beacons. So people living in the Unknown regions could invent navigation systems using the various natural landmarks in space, and navigate easily in the Unknown Regions, while the navicomputers from the Known Regions, dependent on artifical beacons, would be helpless to find their way in the Unknown regions.
Of course people from the Known Regions could establish beacons at the edges of the Unknown Regions, thus enabling them to navigate for a distance into the Unknown Regions, and when they reach the limit of one beacon, build another beacon to extend their range farther, and so on.
And possibly there is a government in the Unknown Regions which has an agency for the purpose of finding and destroying beacons established by people from outside the Unknown regions, so those outsiders won't be able to navigate in the Unknown Regions.