Any good day after Halloween for 2-3 weeks. When I say "good" that is mostly weather dependent. The colder the better and preferably not after a night when the moon was bright overhead.
Interesting you say not after a full moon. Last year I had pretty good action during the days on the full moon. Could almost set my watch by it. Little bucks and does in the morning. About 10am the older bucks would start to move
I could care less about moon phase. I do care about moon rise/set times and level of cloudiness or night brightness.