A lunar base would provide an excellent site for any kind of observatory. Particular advantages arise from building observatory facilities on the Moon from lunar materials. As the Moon's rotation is so slow, visible light observatories could perform observations for days at a time. It is possible to maintain near-constant observations on a specific target with a string of such observatories spanning the circumference of the Moon. The fact that the Moon is geologically inactive along with the lack of widespread human activity results in a remarkable lack of mechanical disturbance, making it far easier to set up interferometric telescopes on the lunar surface, even at relatively high frequencies such as visible light.
The Moon would be ideal site for a space observatory.