For better or worse, Pi Day seems to be already fairly well established. I propose a modified **Pi Day holiday 'weekend'** which would aim to broaden its focus and break some of the stereotypes your question concerns, while cashing in on its 'name recognition'.

*March 13.* 313 is a twin prime and a palindrome, so there are plenty of ways we could go with this, although I can't think of any specific activities. It might be fun to kick off the festivities with an organized **Trimathlon** event - that is, some sort of grand scavenger-hunting, puzzle-solving, team competition.

*March 14.* **Pi Day**. I'd like to second the recommendation of Buffon's Needle related activities for this. 

*March 15* happens to be **Leonhard Euler's birthday**. As Mensen suggests, celebrating individual mathematicians helps humanize the discipline. Perhaps a famous-mathematican costume contest? Euler's contributions in particular are another source of activities; the video game *Katamari Damacy* is a great one to do with exponential growth.

EDIT: *Removed a couple overly cynical remarks in the first paragraph expressing skepticism about whether alternatives would catch on with the general public.*