No one here is on an ad com, so no one can tell you your chances. Look at the profiles thread and see what it takes to get into those schools you want. But if you want an honest response your chances at Princeton and co. are minimal: you could be ramanujan reincarnate and it would still be a crapshoot. You should apply to at least one, but don't count on anything. Anything else would be guessing: if I were you I would apply to the bulk of my schools in the top 20 with at least one top 6, and at least one safety in the 30s. Make sure you apply to many schools. Like 10+.
Research is critical if you want to aim that high. You have REU's, which are great, does your school have a senior thesis thing? A summer long project is great, a year long project is fantastic. My thesis is probably a major reason I got in anywhere, if only because it gave me a top notch recommendation from my advisor.
[My senior year, I've been taking 5 math classes each semester, including the thesis and a grad class

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