I like the idea of manufacturing spacecraft parts on the Moon. There is no oxygen so metallurgy may be easier, gravity is lower, so some alloys should be easier to make and there is abundant energy in the form of sunlight. I don't know about its mineralogy, but I would suspect it's rich in light metals.

Also, a radiotelescope on the far side would be shielded from Earth's interferences.

And, of course, someone has to bury a big black brick in Tycho so future generations can be puzzled.