I genuinely enjoy volunteering and want to dedicate a good deal of my time to it. The thing is, everyone volunteers. I want to make myself stand out somehow, especially because I’m wanting to apply to top schools. Since the place I volunteer at (a museum) largely focuses on STEM, I was thinking of organizing a few events over the next couple of years about mathematics (what I plan to major in). That will be really enjoyable for me, but should I be doing more? I just feel unimpressive because I’m not and don’t want to be the president of any club, on student council, in sports, etc.
If that’s what you want to do, then go for it. 
That sounds absolutely excellent! Do your own thing- pick a topic in math that’s really fun!- and it’ll make you more impressive than anything. Not to mention, volunteering at a museum is pretty cool in its own right.
Don’t worry about how impressive you are. Instead, think ‘oh, that’s really handy’ when you realize something big, that you’re passionate about and very well could do, would be pretty interesting on an application. Don’t do anything you wouldn’t do anyway.
Edit: this is an article I’ve read that I see (unsurprisingly, given the nature of this bunch) get passed around a lot on CC. It is excellent, relevant (mostly) everywhere, and way applicable to your dilemma
http://mitadmissions.org/blogs/entry/applying_sideways
High school is a chance for you to discover who you want to be and what you want to spend a large portion of the rest of your life doing. If you are not going to enjoy being on student council, or if you are not passionate about playing hockey, then you should not spend time trying to make your resume look impressive with all of that. It sounds like you are definitely on the right track to making your high school experience your own and that is what is really important.