Much easier to build on the moon than optical telescopes: radio telescopes.
Find a nice 10-20mile diameter crater and spray an ultra-thin layer of metal, mount a receiver on a really tall mast in the middle and you've got a SETI machine that'll outperform anything on Earth. Put it on the backside of the Moon in the shadow of Earth's continuous storm of radio waves and listen for ET civilizations halfway across the galaxy.
The astronomical work you could do with a 20mile-diameter radio telescope would be enormous and it would be far easier than building an optical telescope.
A far better start for the money.....