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 also suspect that the idea of math being about "voodoo numerology" is part of a broader, preexisting stereotype. If this is the case, other math holidays may not have much of a chance gaining traction while still remaining 'true'. The best part about Pi Day is that people pay attention to mathematics when they otherwise might not and we have an opportunity to break some of these stereotypes.
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.