Also one more thing here. People keep saying put a telescope on the moon. No. This is a terrible idea. The moon has no air, true. It also has gravity. You need to land on the surface. Then you need to take off again. And lunar dust is a pain in the ass to work with. Think of talcum powder, but made of razor blades. It gets everywhere and screws up motors and joints. Also you are limited to the part of the sky you can watch due to being on the surface of a sphere.
For the same money you can make a better telescope (radio, X-Ray, Infrared, Optical) and put it in orbit. One of the reasons that they are going to put the James Webb in orbit at the L2 lunar node is that the earth and moon block the sun creating permanent shadow to keep the telescope cool (James Webb is an infrared telescope that can also barely go into the visual range. Infrared needs to chill and cool the detectors as much as possible).
Same thing with Mars. The Martian surface is a bad place for a telescope. A very fine dust delivery system, an atmosphere to deal with, and at the bottom of a gravity well.
For the money of a space telescope we can do better on the earth's surface, but there are major drawbacks. None of the ESA/ESO telescopes in Chile, for example, can observe M51, M101, M81 or the Andromeda Galaxy. These are the closest large galaxies to us, but they are too far north; the earth blocks them from view. We have giant telescopes in Hawaii that cannot get a good view of the stuff in the far south, same reason.
If we do this, in space, in orbit, that is the way to go.