To follow up a little on what Elizabeth said, there are some rules of thumb for when the moon is well-placed for photography. The moon, like the Sun, travels a changing path throughout the year. You want it as high in the sky as possible when you shoot. Here's a rough guide to the phase that's highest in the sky in a given lunation:
Spring: first quarter (waxing) right after sunset
Summer: new moon (not much good for photography)
Fall: last quarter (waning) just before sunrise
Winter: full moon around midnight
Here in northern Arkansas, the moon can get as high as about 7 degrees from zenith which, besides giving you a crick in the neck, minimizes atmospheric distortion. I use Starry Night for my planning, but there are lots of software packages that will do just fine, including the free ones mentioned in this thread.