Moonlight is 250000x dimmer than sunlight, but you can still see things illuminated by moonlight once your eyes adjust.
Neptune is 29 AU from the Sun, so by inverse square law, the sunlight is 29^2=840x dimmer on Neptune than Earth. Visibility should be decent out there. Neptune will stand out pretty well against the perfect blackness of space.
Hmm, I've always figured it's a bit of eyes blurring "bright" lights (the stars you can see), and a bit that there are lots of really dim stars that you can't really see, but add in some light.
I wonder how dark it would be out there if you saw it with your own eyes. I would guess it’s pretty dark.