Well, I was told by an astrophysicist on /r/askscience, that inside of 1.5x of the event horizon, there are no more stable orbits (you either go hyperbolic, or fall in). Outside of that distance, you can absolutely orbit a black hole just like any other body, with the same chances of outside forces influencing your orbit.
He shouldn't have used the word "stable". Orbits from 1.5x the horizon radius to 3x the horizon radius exist, but they are unstable, like a pencil balanced on its point; any small perturbation will cause the orbiting object to either fall into the black hole, or fly off to infinity. Orbits at 3x the horizon radius or larger are stable in the sense that small perturbations do not do this; the object will just tend to adopt a slightly different orbit.
Since the post I was responding to used the word "safe", I was not including the orbits from 1.5x to 3x the horizon radius, since they are not, IMO, "safe"; you'll need rocket power continuously available to avoid falling into the hole or flying off to infinity due to small perturbations.
(A link to the askscience thread would be nice, btw.)
