I'm probably misunderstanding the question, but
notes that Neptune's magnitude from Earth is 7.8 at opposition, when it's
4347.31 million km away.
If you get 3 times closer, 1449.1 million km away, Neptune
will appear 9 times brighter, bringing its magnitude to 5.4,
well within our visible range.
As Stellarium notes below, Neptune is almost visible
(magnitude 5.66) from Uranus, an entire planet away.
My version of Stellarium can't simulate the view from Naiad
(Neptune's closest moon), but at a distance of only 48,227 km
(Naiad's semi major axis), Neptune's magnitude would be almost
-2, much fainter than our own moon, but brighter than Sirius
appears to us.
This brightness would be spread out across Neptune's disk, but
the brightness at any point would be about magnitude 3, still
Moreover, Naiad probably has a much thinner atmosphere (and no
light pollution), making Neptune even easier to see.
The other outer planets are visible from Earth (Uranus just
barely), and so would also be visible from their own moons.
I haven't done the calculations for Pluto, which is
technically no longer a planet.