Only the human colonized worlds will have stations and hence be viable for trading, missions, bounty hunting, or piracy. Those systems are probably just a subset of the systems with real distance and star spectral data from the Hipparcos catalog (118,000 stars within 650 ly). Human space is centered on the birthplace Sol, and as you'll note from the Galaxy Map, extends in radius little farther than Achenar, the Empire capital, at a radius of 43 pc = 136 ly from Sol. In a sphere with a radius of 43 pc, there are roughly 330,000 systems at the local density (~1 star / cu pc), but the numerous (80% of stars) but dim M class are poorly represented that far out in astrometric catalogs.
So, my guess is there's under 10,000 colonized systems, and further guess around 25,000 players online at any given time (optimistic, comparable with EVE). Those estimates suggest 2.5 players per colonized system, but players will be highly concentrated in trade hubs or systems in conflict or transition. So at any given time, most human systems will be empty of players, but a few dozen will have hundreds of players, perhaps thousands.
Outside of that core of colonized worlds, there will be exploration teams ferrying fuel and repair supplies to explore points of interest: Ie, Beta Lyrae (960 ly), Orion Nebula (1344 ly), V4641 Sgr (1600 ly), perhaps even Sgr a* at the galactic core (26,000 ly). Their only contact will be with fellow team members and perhaps the occassional Thargoid.