For better or worse, Pi Day seems to be already fairly well established. Getting broad recognition for a second math-related holiday seems like a pretty daunting task. I'm skeptical that the (admittedly awesome) alternatives will be able to gain traction among the general public, in part because the problems you bring up about Pi Day may have deeper roots in preexisting stereotypes. On the bright side, I do think that Pi Day provides us an opportunity to break some of these stereotypes as people are paying attention to mathematics when they otherwise might not.

That said, it'd be great if Pi Day had a broader focus than a single constant. I propose a **math holiday 'weekend'** around Pi Day so we can include all of mathematics in the celebrations!

*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: *Clarified a couple overly cynical remarks in the first paragraph.*