ESA publishes quite a few images from the 67P comet, sent by Rosetta, from various distances away to collect as much as possible and as varied as possible.
As I write, Rosetta is 6 Km away from the comet, and can even take clear pictures of its own shadow on the comet.
The comet does spin though, and dust may prevent Rosetta from getting too close or entering some cone formed by the comet's tail (there are related questions).
How close could Rosetta theoretically get to the comet?
The question may not be so easy to answer, as the comet is not spherical, and its spin may not be planar.