-The moon has no atmosphere and as such it makes astronomy much easier.
-The gravity well is MUCH smaller for the moon than Earth, and so it makes a good launching point for other places.
-This isn't for NASA, but for the human race. You know that saying about "don't put all the eggs in one basket"? Well, right now, ALL of humanity is in one place: Earth. What if something catastrophic, natural or man-made, happened? All humanity could perish. By spreading up and out, we assure human life will survive even if Earth goes dead.