If I apply to 10 undergraduate schools what're the odds I get into AT LEAST ONE?

I love MWolf’s comment (#32). Explains the issue clearly and knowledgeably.
OP: As others have said, I suggest that you concentrate on targets and safety schools. Even Olympic athletes and children of billionaires need to show that they can do the work at an Ivy or Stanford, and a 3.3 GPA is unlikely to convince those types of schools that you are qualified academically.
I think that NYU (which you mentioned) could be a good fit for you. You could also look at George Washington, Bryn Mawr, and Smith. It depends on the type of school and community that you’re looking for.
There are plenty of excellent schools in the NW. I suggest looking at UW, though Foster (business school) is more difficult to get into than Arts & Sciences, where you could choose economics. Private schools to consider are Seattle U (Jesuit, but not much focus on religion and an emphasis on service), Whitman, Reed, and Lewis & Clark. Public safeties include WSU, UW Tacoma, UW Bothell, and Western Washington. I agree with another poster who suggested Evergreen, given OP’s interest in Gallatin. If you want to go to California, consider Santa Clara, Mills, Pitzer, and possibly Scripps (though probably a reach).
You have a lot going for you, and despite the bumps early in your high school career, you can get into an excellent college and succeed.