The Emperor's psychic beacon, of course.

I’d use Discworld nomenclature:

• Hubward
• Rimward
• Turnwise
• Widdershins

Cosmic background radiation provides a stable frame of reference for setting up a coordinate system. If the explorers have a main HQ base, it can be set as the origin (0,0,0). The location of an object in space can be communicated using a tuple like (10km, 30°, 30°), representing the radius (distance to the object), polar angle (angle between the positive z-axis and the line connecting the origin to the point), and azimuthal angle (angle between the positive x-axis and the line connecting the origin to the point on the xy-plane).

Alternatively, if only a general region is needed, grid coordinates can be used with any useful unit of measurement for the distance between grid lines.

Center of gravity of the galactic cluster/supercluster

::: spoiler It will be so much more complicated than "North" IMO. We will use something like XNAV. It becomes a measure of time as much as any measure of location, along with a measure of relative gravity.

I don't think space exploration in the current culturally adolescent fantasy of a naval voyage type of experience will ever happen. I believe we will traverse the stars, but it will be long after most of humanity lives in O'Neill cylinder like space habits, primarily in cislunar space. The big shift will come after we have effective infrastructure to access the vast resource wealth, first in near Earth objects, then in other small bodies such as Ceres if it is fully solidified, or other planetesimal cores that are accessible. Gravitational differentiation of heavy elements sequesters almost all of Earth's resources. We are fighting over the scraps of a billion years or so of smaller collisions on the skin of Earth that happened to remain accessible, and did not get subducted by plate tectonics or buried too deeply to access. Undifferentiated bodies from the early stellar formation should be much more abundant in mineral wealth, and a planetesimal core, should absolutely dwarf most mineral wealth humans have ever scavenged.

Once we get to this stage, I don't think we will leave until Sol starts causing problems that harken a coming distant end to Sol. At that point, I believe we will build a massive infrastructure to produce antimatter in quantity and generation ships for one way travel.

In that scenario, navigation in a human sense is largely irrelevant. When we are interstellar travelers, the destination will be our guiding star. I believe we will likely also create something like kilometers scale self replicating systems for resource acquisition and processing. These will need to navigate within a stellar system. For those use cases, maybe they would use something like XNAV as a backup, but they would likely use two way communications beacons with something like an all talk and listen all the time type of management. I think this kind of communication will likely be critical for all human colonies as well to ensure cultural unity. I don't think we will ever travel the stars. Space is far too vast. I think FTL or even a substantial percentage of it is pure fantasy. One of our biggest issues with the concept is that we call it FTL. Light is not relevant here, it is just a shortcut term that is not relevant to the real issue of the Speed of Causality. Light can travel at the SoC, but the SoC has no inherent need for or relationship to light as a fundamental property. If no photons are present the SoC marches on.

I view the present sci-fi navel drama trope like the naïveté of 15th century Europeans saying "We'll just sail around the world backwards for a new trade route to India." Reality is far more complicated and beyond the scope of anything these leaders imagined possible. ...but that is my $2 comment when you only asked for $0.02. I really like the subject of futurism, and like to expand upon the abstracted ideas. I'm certainly no expert. This is part of a creative writing hobby project and I'm always open to adding complexity or changes with new information.

If we're talking intergalactic navigation, I'd use QSO J0529-4351 as north.

It has the highest chance of being visible from wherever we want to go.

I don't think it really makes sense to have a north as such. The only potentially exception I can think of is more of a definition of 'up' rather than north and pertains to hemispheres of bodies.

You would likely start from the center of your galaxy, then pick a culturally relevant star near the outskirts, in our case Sol, and call that, well, something (Solbound?) Then work your right angles from there. You could pick other cultural stars in the other directions too.

Most galaxies are pretty flat, so you'd probably have to reference a conveniently positioned other galaxy for your up and down.

Earth, obviously. Or rather, where we think we left it...

So i guess what your asking is what is the stationary point of reference that you use to calculate your position? You can use any object but typically you use whatever object your gravitationally bound to. Like in earth orbit you use earth, in interplanetary space you use the sun, in interstellar space it becomes more up to you. Center of galaxy maybe, or nearest star. Kinda depends what ur trying to do.

Probably arbitrarily one of the two vectors perpendicular to the plane of the Milky Way? (Assuming it wasn't necessary for this navigation system to work outside of our galaxy.)

We could assign it to any point within a recognizable region in the Cosmic Microwave Background, which would probably be the most universally-applicable reference available. One just needs to be able to filter out the noise from surrounding celestial bodies. The CMB does slowly change over time, but so too does the position of stars within galaxies and galaxies relative to one another.

Point it towards Earth, or if that's impossible with future space magic, towards the largest gravity well, i.e. center of the local galaxy or nearest dense object.

Might be a bit simple but why not the "North Star" (Polaris)? Navigation could work via analysis of stars positions relative to eachother/positions of constellations relative to the ship. You could justify it in-universe as being a nod to how early mariners used these same stars to navigate Earth's oceans.