My chances for gaining admission to the following colleges? Given conflicting advice.

I am a Pakistani student studying at an internationally recognized American school in a remote area in Saudi Arabia who does not need financial aid. My major will be chemical engineering. The colleges I will apply to are:

-Princeton University

-New York University

-University of Washington

Academics:

UW: 3.73. W: 4.02 At a school known to be rigorous.
SAT: 1st: 1250. 2nd: 1420
AP: School only offers 4 courses in total. Taking 2 of those this year. Previously, AP language 4 and APUSH: 4.
Salutatorian

As there are VERY limited opportunites for extracurricular activites in Saudi Arabia, I have tried my best to be as involved as possible. Some highlights are:

President of Student Council (4 year member)

2 years of NHS

5 years in JV basketball (captain, co-captain)

3 years in JV volleyball

MUN (Best Delegate)

Research on ways to better utilize natural resources and to treat water.

Volunteer work includes various religiously affiliated activities

Great Go-Karter (racing for years)