To what extent may you repair the green prior to your putt?

Since I play a lot of muni courses, and mostly on weekends and in the afternoons to take advantage of the twilight rates, the greens are usually pretty thrashed by the time I take on the course.

My question is: to what extent do the rules of golf allow me to repair the greens prior to putting? I assume I can fix pitch marks and remove loose impediments in my putting line (can I even do that?).  How far can I go in ensuring that my putt doesn't fall offline by a man-made obstruction?  Can I repair spike marks? What about huge tufts of grass?

What you said is what you can do.  You  can repair any pitch marks on the green and remove loose impediments and movable obstructions. That is all - no repair of spike marks, no repair of damage not caused by a ball.  No relief for growing grass - that isn't an abnormal condition.

If you play with friends in a casual group (meaning not a tournament or competition) you can decide if damage done by some idiot smacking the green with his putter in anger is deserving of repair as that is something which would usually be referred to the committee for resolution.  In my casual groups we are more likely to take relief for line of putt, then report the damage to the pro shop immediately after the round.

I played most of my golf on a muni (which fortunately became better as it matured over the years), so I know what you are talking about and it's just something you live with.