Is it possible to see Callisto with the naked eye when it's at its greatest elongation from Jupiter? A quick search shows that Callisto has an apparent magntidue of 5.65, which would make it easily visible under relatively dark skies. Being the farthest Galilean moon, does it ever get far away from Jupiter for it to be discernable to the naked eye?
This has been an area of controversy for quite some time now, with no clear resolution (if you'll pardon the pun). There's been interest in supporting or refuting claims that observers were able to see the moons with the naked eye before Galileo. There are, of course, two major impediments (which you might well know about): brightness and angular separation from Jupiter.

The human eye has a diffraction-limited resolution of (roughly) one arcminute, whereas Callisto can reach separations from Jupiter of about 10 arcminutes - so, arguably, resolving it is not an issue, as it is with some other moons. However, we do have to deal with the problem that light from Jupiter could dominate any light we see from the moons (even if Ganymede and Callisto are too close to be separated and appear as one source). It's the same issue we get when observing faint sources near bright sources using a telescope, such as direct imaging of exoplanets.

If you do want to give this a shot, you might want to block out Jupiter's light with some foreground object, while making sure not to block out the moons. Choose a dark night when Callisto is at its greatest separation, and you might have a shot.

But not great odds, of course. I'd be surprised if you succeed. On the other hand, get yourself a good pair of binoculars and you won't have a problem.