What are my chances for MIT, Caltech, Cornell and Princeton?

I have a 3.67 GPA (only including core classes, 3.8 including engineering, health and phys Ed) but I have perfect scores on SAT. I self studied and took AP tests not offered at my school (4–5 on all of them). The AP tests are: all 4 physics exams (5) Calc BC (5) Stats (4) Bio (4) Chem (4). I had a B+ in bio as a freshman, 710 on the subject SAT. A- in Chem (sophomore), 760 on SAT, A in honors physics and all my math classes (800 on Math II and Physics). I got A-s and an A in Spanish, B+s and an A- in English, A-s and a B+ in history (we had to memorize things and I wasn’t very good at that). In freshman year, I took linear algebra and discrete mathematics at my school. (A+). In the summer between junior and senior year, I took Calc III and Diff eq at my local community college, and Intro to Number Theory at Stanford OHSx (As in all of them). Most of my senior year courseload is pretty standard, my science is AP envi sci. However, in fall, I am taking Modern Algebra and Modern physics, and in the spring I am taking Intermediate Mechanics I and Real Analysis (Stanford OHSx).

My Essays are compelling (my friends said they are very honest and open) and I will have one amazing rec letter, one great rec letter and 3 still really good rec letters.

My ECs are as follows,

I won a national award at the VEX Robotics US Open in 2015 (I am VP of VEX in my school)

I am president of science bowl, I tripled the size of the club and turned it from a single team into an actual club with weekly meetings

I won some awards playing USTA tennis tournaments, not very spectacular

I started/organized the physics olympiad, Princeton physics competition and physics bowl at my school

I placed 4th in the state in Physics league

I am a coach of my school’s math league main team (we have an excellent team, last year 11 people qualified for ARML, including me)

We were one of the top 10 teams at PUMAC in the B division

My AMC scores aren’t that great, I missed AIME by 1/6 of a question (I always run out of time)

I organized a bone marrow drive at my temple recently and I have been volunteering there for a while now.

I am enrolled in the Columbia Science Honor Program

I also participated in research over the summer and wrote the beginnings of a paper, but its not finished or published.

I had an independent research idea in physics which I am currently working on under the guidance of a CalTech PhD student

I am getting rec letters from the professor I worked with as well as the PhD student.

I worked as a math tutor at Kumon for about half a year

I have a few other academic awards like 1st in my county for Merck Science day, TSA TEAMS top 10 in the country in problem solving, etc (but these will probably not be on my application- or maybe one of them might be).

no for caltech, prob no for mit, yes cornell, hard for princeton

Anyone else? With more detail?

I think you have a good shot at Cornell, but I would pick a few safeties.

What about UC Berkeley Arts and Sciences or UChicago?

GPA will affect your admissions to these schools.
They want students who can do everything well, not just the STEM stuff.

Caltech is very by the book on gpa and scores so I think that is very unlikely. MIT it’s hard to tell. They will want to see the scores from the math comps be in the highest ranges but if they value the physics comps it might balance out. Does your school rank? That could be the deciding factor in terms of GPA issues and MIT. You really need schools that look more holistically. If you are planning on majoring in physics UChicago while still a lottery is a great physics school and tends to be more holistic and forgiving of GPA issues than some of the other top schools if you appear to be a good fit. Cornell is a solid maybe unless your class rank is a low percentile. I think Princeton is unlikely. Do you have some matches/safeties? William and Mary has an up and coming Physics department but GPA still might be issue.