YU undergrad is a self-selecting program. Everyone in the undergraduate program is an Orthodox Jew, and the school itself caters to that demographic. The undergrad school is split into two parts, The Yeshiva College for Men in Washington Heights, and the Stern College for Women in Midtown (a several mile separation). I can only speak for the men's college (since I am a male and many of my friends are attending or planning on attending the place). The morning is all intense Judaic studies, with regular classes not starting until 3:00 P.M. Those classes could go as late as 8:00 P.M, and with extracurriculars, the hours could go even later.
Now that those formalities are out of the way, I'm gonna be frank right here. It's a HUGE deal whether you're Jewish or not. As I said earlier, there are non-Jews in the undergraduate program that I know of, and I'm pretty sure there haven't been any in the undergraduate program ever. You would definitely feel like an outsider in the university, especially considering the relative insularity of the Orthodox Jewish community. Many people choose to attend YU over CUNY because of its religious Jewish nature.
For your case specifically, the graduate schools are MUCH more diverse, with many non-Jews of all types attending the schools to study their various professions. As mentioned in another post on this thread, Einstein is no longer giving YU granted degrees, as it's now its own independent medical school I believe, and a very highly regarded one too. While there will still be Jewish elements in it, like Kosher food, and observance of the Jewish holidays, the pervasiveness of Judaism is NOWHERE NEAR the level of the undergraduate schools. For your purposes, going to CUNY and following a pre-med track and doing well will get you a good shot at Einstein (if that is the medical school you choose to study at) without the probable hell you would endure as a non-Jewish YU undergrad, and for a mere fraction of the cost.
I hope this was helpful to you and I wish you the best of luck in your college search!!!