It would depend on how far out you want to drive. Missoula has a 4 wheel club you coud ask: Mountain Backroad 4x4 club is one, or Montana 4x4 Association is another. And yea it can also be a tourist with the college. I would say look at heading maybe further north outside or even west side to find trails.
Showdown and possibly Anaconda or Deer Lodge? They have hunting so I'm sure there would be trails up that way to.
i have heard of the montana 4x4 doing a divide ride looks pretty cool. Kings hill is just before showdown its where i snowmobile there are a ton of logging roads around there and the off the beaten path roads its mabye hour and a half from great falls good to go and camp and play. Never had the time in missoula to go out and explore alot but i got friends that take off on some roads i have seen pics and the roads look like there build for a jeep lol. Havent gone up by andaconda or deer lodge alot but another one is cascade there are a few fun roads out there.
Have you been out by lolo at all i have been to the hotsprings a few times never in my jeep sence i just got it.
I'm in Colorado now, have been since 1993, but I still keep up with my family that lives up there. My cousin takes his truck four wheeling, I'll have to ask where he goes. And I know my aunt and uncle take their ATV on some back roads in Helena.