With your interest in continuing your work at MSKCC, these are the schools I would look into, and how I would categorize your chances for admission. I am known as being on the conservative side with my estimates:
With the CUNYs, I’d also recommend applying to the Macaulay Honors College. Also, although you are aiming for an MD/PhD or a free medical school option, realize that those are extremely competitive. If you seriously want to go to medical school, I would make sure to include options that will be very affordable in order to have extra funds for medical school, should you decide on that path. I would not be surprised if you received extremely generous merit aid from some of your likely options.
Extremely Likely (80-99+%)
- CUNY City College
- New Jersey Institute of Technology
- Seton Hall
Likely (60-79%)
- SUNY Stony Brook
- CUNY Hunter College
- Rutgers – New Brunswick
Toss-Up (40-59%)
Low Probability (20-39%)
Lower Probability (less than 20%_
- Columbia (NY)
- NYU
- Princeton (NJ)
Now, research in a lab is available at just about every university with a science department. So, excluding the MSKCC wish, these are some schools that you might want to consider.
Extremely Likely (80-99+%)
- U. of South Carolina: Also has a very well-reputed honors college.
Likely (60-79%)
- George Washington (D.C.)
- Howard (D.C.): HBCU, which is also has a really good science scholars program that @ChangeTheGame may be able to speak more about.
Toss-Up (40-59%)
- U. of Rochester (NY)
- Wake Forest (NC)
Low Probability (20-39%)
- Boston College (MA)
- Boston U. (MA)
- Northeastern (MA)
Lower Probability (less than 20%)
- Rice (TX)…not east coast, but right next to Houston’s medical area, including the renowned M.D. Anderson Cancer Center
- Brown (RI)
- Cornell (NY): I believe that one of the publicly-subsidized colleges also has some good options for science/med school prep, which might be a less competitive entrance and be lower cost. I can’t remember who was discussing it recently, though to tag them.
- Georgetown (D.C.)
- Georgia Tech
- Harvard (MA)
- Johns Hopkins (MD)
- Yale (CT)