At what distance would it be safe for humans to stare at the sun? Let's say we could travel anywhere in the solar system, at what distance would it be safe for a human to stare at the sun (without eye protection) and not get eye/retina damage?

(Not sure where this question is good for, here, or perhaps Biology.SE, so let me know.)
If the sun is visible as a disc, then it is certainly can cause damage. As you move further from the sun the disc appears smaller, but the surface brightness remains the same. The eye can resolve a disc of about 1 arcminute, and the sun is about 30 arcminutes when viewed from Earth. So you would need to be at least 30 times further from the Sun than the Earth is, which puts you almost exactly at Neptune.

From that distance, the sun would be a magnitude -19 star. If you stared at it, it could probably still damage your eyes, however, your eyes are constantly jumping (saccades) which might move the image of the sun around the retina enough to prevent damage. There is, of course, no atmosphere to protect you from UV, so let's hope that's not a problem.

Beyond Neptune the sun gets dimmer, as it can't appear to get any smaller, and there is probably little risk by the time you reach the main part of the Kuiper belt.