In general Damon, the absence of the Moon in the sky is best. Unless, of course, you want to cruise the Moon's surface or go looking for lunar occultations!
The effect of the Moon is to wash out the sky with moonlight, generally all over, thanks to our atmosphere, but particularly bad close to it. Fainter objects just won't have contrast against the brighter sky.
However, visitors trip over things less and it is easier to find what you have dropped.
But, for observing some things, the Moon is not a great problem. Venus, Jupiter, Saturn - the presence of the Moon is no hassle. Looking at bright stars, open star clusters and splitting popular double stars - also no great problem. But the moment you are talking about nebulae, galaxies, globular clusters - you want to say "Bye bye Moon".
When you are showing people the sky, it is often useful to pick a night with some Moon around - a few days after new Moon is usually good. They can have a good look at the waxing crescent Moon, then as it drops low in the sky, fainter objects can be seen.
