My experience with the last interview cycle may be a little blunt, but I'm only saying these things because I went through a situation kinda like yours.
Matching into NYC schools is generally tough. Though there are several programs, each program does not necessarily have many spots. Columbia only has 3 spots, while NYU has 7. I read or heard somewhere (either on their website or through another applicant) that NYU strongly prefers applicants from the New York area or go to a school close to NYU. Cornell seems to have some diversity in their residency pool, but they only take 3 residents a year. In addition to that, they came from some pretty good medical schools (at least per US News ranking). So ultimately it goes like this:
1) Are you from a top 25 or even a top 50 medical school?
2) Do you think your application is competitive enough?
3) Do you have some strong connection to New York? When I mean by strong, I mean by family, relatives, or have lived there for several years. Liking the city isn't going to cut it.
4) Is your personality charismatic enough to dazzle the entire staff and secure an interview? Be honest with yourself too.
5) Do your letters of rec come from a big hot-shot in the academic community of ophthalmology?
If you've answered no to at least two questions, then if I were you, I'd reconsider one of your away electives. I've always had the philosophy of that anyone can play with the big boys if he or she tries hard enough and has the will, but realistically you should also try to successfully match. In the end, what's more important than matching into a successful ophthalmology program is to 1) match and 2) not match at a horrible program.
However, considering that it's July 19th, I'm not sure how viable it would be to change one of your away electives if you wanted to. Ophthalmology away rotations are tough to secure, especially in August. Your September away elective may be easier to change, but you should also know that by that time, securing a letter of rec from that program for your application is pointless, because it will be too late. It will be good primary to get a 4th letter of rec to bring with you, or to secure an interview there if you perform well.
I really hope this helps. This process is humbling, tiring, and expensive. You should know all the information up front, truthfully, so you aren't set up for false expectations.
