The issue though is what are you going to do with a moon base? The moon does not hold any significant resources which are useful in the further exploration of the solar system. (Now, I don't know how much water there is on the moon, but my guess is that it isn't enough of it to justify building a moon base just for the water.)
Astroids, comets or Mars, that should be where the action is. :)
Due to the exponential nature of the rocket equation the most important resource needed for exploration of the Solar System is rocket fuel.
Water can be turned into rocket fuel by splitting it into Oxygen and Hydrogen. Water and Oxygen are also very important consumables in spaceflight. Moreover, Oxygen and water can be used to grow food.
It can be an order of magnitude more efficient to launch propellant from the Moon than from the Earth. Given that, it starts to make sense to launch unfueled spacecraft from Earth which fuel up with Lunar sourced propellants (and other consumables) at a depot in Earth orbit or Lunar orbit. With such a system you can use smaller, reusable launch vehicles from both the Earth and the Moon to build a self-sustaining trans-Earth exploration infrastructure, rather than continually building one-off efforts to get to Mars, the asteroids, etc.
I think a large part of the justification for a moon base is that it could be used as a location from which to stage further space missions. If you construct a rocket on the moon you've got no atmosphere and a fraction of the gravity to deal with.
No atmosphere might also make it useful for astronomy, but I'm not so sure of that.
A lunar base would provide an excellent site for any kind of observatory. Particular advantages arise from building observatory facilities on the Moon from lunar materials. As the Moon's rotation is so slow, visible light observatories could perform observations for days at a time. It is possible to maintain near-constant observations on a specific target with a string of such observatories spanning the circumference of the Moon. The fact that the Moon is geologically inactive along with the lack of widespread human activity results in a remarkable lack of mechanical disturbance, making it far easier to set up interferometric telescopes on the lunar surface, even at relatively high frequencies such as visible light.
A lunar base could also hold a future site for launching rockets, to distant planets such as Mars. Launching rockets from the Moon would be an easier prospect than on Earth due to the Moon's lower gravity requiring a lower escape velocity.
Astroids, comets or Mars, that should be where the action is. :)