What I would sci-fi utlimately love is the combination of both. Putting permanent bases on the moon, and then building whatever the sciencey word for lunar telescopes. They get the benefits of no atmosphere, and the benefits of being on the "ground" so things can be updated/fixed compared to just floating in space.
Makes no sense to me. Given you'd have the capabilities to have bases there, you'd also have the capabilities to fix stuff floating in space effortlessly. Btw. ground can shake or vibrate, which is no benefit at all.
edit: also electrostatically charged, abrasive dust particles.