Rate my chances at Princeton??

I am the first child in my family to go through the admissions process and am soo lost on whether or not I should even keep dreaming about Princeton. It would be GREAT if I could get some feedback on what I should or should not expect.

Junior as of now.
Asian girl.

Objective

SAT I (breakdown): overall 2260, CR 690, Math 800, Writing 770 (first sitting)
ACT (breakdown): NA
SAT II: Math II 800 (planning to take more of course)
Unweighted GPA (out of 4.0): 3.9
Rank (percentile if rank is unavailable): top 5%
AP (place score in parenthesis): AP Comp Sci (3), AP Physics B (4), AP Statistics (5), concurrent enrollment in 7 APs
IB (place score in parenthesis): NA
Senior Year Course Load: im thinking four or five APs and a couple college courses?
Major Awards (USAMO, Intel etc.): AP Scholar, Publication in National Magazine, Various in state publications, National Science Bowl, 1st State Debate, Octas-finalist at national debate tournament, Alternative National Qualifier for Debate (others I will not include for privacy reasons)

Subjective

Extracurriculars (place leadership in parenthesis): Varsity Tennis, NHS, Speech and Debate (2x Varsity Captain), Piano since age 6 (various awards and volunteer work), Local Newspaper (student journalist), Science Bowl (Secretary), Science Olympiad (President)
Job/Work Experience: Certified Nursing Assistant
Volunteer/Community service: church volunteer, senior center, tutoring
Summer Activities: children’s missionary, work, volunteer at senior center

Other

Intended Major: Mathematics
State (if domestic applicant): Out west (not california or texas)
Country (if international applicant): USA
School Type: Public

If not qualified any suggestions for other good schools I would be a competitive applicant for?

I would retake the SAT if I were you, CR is too low. You need better grades in your AP tests; stay away from 3s. And you should be getting high scores in AP Calc AB and then BC if you want to major in math, and probably enroll in multivariable and linear, perhaps at a CC.
It’s definitely not unattainable, but it will be difficult, as for everyone. Keep working hard and you’ll have a decent shot.

agree with avix215, retake SAT

ECs sound very very very stereotypical (piano, NHS, debate, tennis, newspaper). However you seem fairly involved in debate and piano. If you get the SAT to 2350, you’ll have pretty good chances though.