Lunar telescopes are... problematic.
First of all, day-night does not matter much for the observation - shield it from the reflections of the ground, and the sky remains dark anyway, since there is no atmosphere to scatter solar light. But it matters a lot for engineering. The difference in temperature between lunar day and night are... well night and day. We're talking swings from -300°F to +225°F. And since you're grounded, convection matters, so you will suffer the differential.
The actual best locations for such a telescope would be crater on the poles. You get a stable environment, you don't have to suffer from solar or earth obstruction... but you have a fixed view of only half the sky. Meaning you need TWO of them, on the north and south poles, to be complete.
The great advantage of a lunar telescope, though, is that it can be built, as you noticed. You don't send your telescope - you ship individual parts, which can be assembled on site. Potentially, you might even smelt and engineer the mirrors on the spot, which means you can make it much larger. You can service it a bit easier than anything save LEO telescopes. And, since it's anchored and has motors, it's a lot easier to point at any point in the sky in view, rather than the complicated and costly gyroscope maneuvers that are required for space telescopes. A few well-placed solar panels on the ground, and your power supply is good for decades.
www.nasa.gov
