Hubble was first and foremost designed to be serviced in space, unlike other satellites. However, if it was in a geosynchronous orbit on the dark side of the moon, we couldn't communicate with it due to the radio blackout that occurs.
Hubble's instruments also compensate for ambient orbital light, and many observations are taken when Hubble is in orbit on the dark side of the Earth.
The James Webb Space Telescope (originally named the Next Generation Space Telescope), the follow-on to HST, will however take advantage of lower light conditions by orbiting at the Sun-Earth Lagrange (L2) point, which is out past the Moon's orbital path. The Wilkinson Microwave Anisotropy Probe, Herschel Space Observatory and Planck space observatory are already in orbit at the Sun-Earth L2 point.