What are my chances of transferring from a community college for Political Science?

Hey everyone this is my first post so forgive me if there are some errors. I’m currently a liberal arts student with a concentration for political science at a SUNY Community College. I feel as if I’ve grown a lot as an individual and a leader since I’ve first arrived at college and I feel as if I have the capabilities and potential to continue grow as a leader. I’m looking for the best school possible to facilitate this growth.

Info:
SAT: Reading: 490 Writing: 430 Math: 600
These score are particularly strange as Math was traditionally my worst subject, I believe medications may have played a factor in my low scores. I understand these are pitifully bad scores, and I’ve been considering retaking them. However I was under the impression that SAT scores aren’t as big of a factor at this point.

Freshman Year: (I’ve been taking increasingly difficult classes every semester)
1st semester: 2.76 with 16 credits
2nd semester: 3.41 with 19 credits
Extra Curricular: FSA, CAB, Student Senate, Internship at city hall, and more…(Pretty good ECs)
Sophomore Year: (Still more difficult classes)
3rd Semester: On track for a 3.8-4.0, retaking a math class from the first semester where I had poor performance to boost the gpa from a 2.76 to a 3.0-3.2
Extracurriculars: Even stronger extra curriculars this year.

I’m projecting my cumulative GPA to be a 3.4-3.6 by the time I am finished with the Fall.

I’m looking at various schools for political science and am hoping to continue on to law school after I am finished. I understand my GPA isn’t the best for top schools, however I have faced incredible economic and medical adversity, which I now look to as a source of strength and growth. My only regret is that I wish I had realized some things sooner, and I hope it’s not too late to go to a great school.

Schools I am looking at for Political Science:
Buffalo
UAlbany
Stony Brooke
Binghamton
NYU (Arts and Sciences)
Cornell (Arts and Sciences)
George Washington University (Arts and Sciences)
Georgetown
Columbia College

I understand some of these are reach schools, and might be completely unrealistic for entry at my GPA and SAT scores. I understand I can get into pretty much any SUNY School at this point, but I was hoping to aim even higher.

Should I retake the SATs?
Are there other colleges I should consider?
Which of these colleges do I have a chance with? (Even a small one)
What else can I do to increase my chances?

Thank you for taking the time to read my post, I appreciate honest responses above all else.

Pretty much out of reach;
NYU (Arts and Sciences)
Cornell (Arts and Sciences)
George Washington University (Arts and Sciences)
Georgetown
Columbia College

Any school that considers SATs for transfers will really have a problem with those scores. If you want to apply to colleges that ask for SATs, take a SAT prep class and try again. I don’t often recommend a prep class, but I think with scores that low you would benefit a lot.