I just got an invitation to a new event series that I was told would take place on the First Tuesday of the month. However, I already go to two different dinners that take place on the First Tuesday, and I suspect that was no accident. For social events, people use the weekends, and for other events people prefer the weekdays. They have a psychological desire for the first week of the month.
So I ran a quick set of yahoo queries to find out how many hits there were on the web for "first monday" and similar strings. I figured that would tell when the most events do occur, and help people pick a day that is likely to have the least conflicts.
The results are below: