Good question, but you're not going to like the answer. The moon doesn't quite operate on a 24-hour cycle like the sun as both moonrise and moonset gets later each day. At least for the next couple of months, as the moon approaches full, it will be up all night.
That cycle also doesn't quite align itself with the clock either, as the last new moon of 2003 (December 4) is above the horizon at night, while the light last full moon of 2003 (December 19) is wasted on the daytime.