I have heard the phrase that you gotta go to NYU because of Bellevue many times. But I always have some doubts about it.
Med students are here to learn the common diseases such as myocardial infarction, alcohol detox, depression, bipolar, appendicitis, stroke, stomach virus, neonatal hyperbilirubinemia, etc. and NOT to learn about digeorge syndrome after thymus transplant, chromosome 16 imbalance, porphyria, etc. I have followed patients with the latter group of diseases but they are not the bread-and-butter cases and they have only enhanced my knowledge base minimally.
When you are on call, the residents are always looking out for the bread-and-butter cases for you to follow because those are the cases you will see for the rest of your life. If they intentionally ask you to follow the zebra (i.e. the once in your lifetime kind of cases), then it might even hurt you in the long run. These rare cases are rare, as simple as that. They can probably form a small part of your training later on as residents, and even when you encounter them for only the second or third time later on as an attending, you will still need to read up to "remember" how you managed the patients before. However, they should have little if no place for you as a medical student.
Therefore, I get suspicious when people keep on espousing the greatness of Bellevue and its immense spectrum of diseases you will encounter there. Sure, some of their names might make an impression on your brain after you hear them on the round for a second or two but they are not very useful for medical student education purpose.
Most hospitals affiliated with a med school are tertiary centers and WILL have enough cases to keep you busy. I don't see why Bellevue should play such a big role in one's decision because Mount Sinai hospital, NY-Presbytarian, etc. will give you enough cases to keep you busy. In fact, Bellevue has poor ancillary services and you will get scutted out. As a medical student, you still need time to read and absorb. Doing a few scut works here and there will be good for you when you are a resident and have to do them yourself. But too much scut work will drag your knowledge base down, way down.