Mt Sinai Hospital is at 98th Street to 102nd Street between Madison and Fifth Avenues on Manhattan's Upper East Side an area that is accessible from many parts of New York City. How near do you want to be? What other requirements do you have? I don't specialize in rentals but might know of a few available if you let me know more details such as the above and price range etc, also I would be glad to refer you to someone who does. Also you could look online for brokers who advertise rentals but please do make sure that the person is a licensed real estate agent with a broker and make sure that before applying for an apartment that you have good and clean credit and other qualifications otherwise you could wind up paying a non returnable credit check fee with some brokers. Here is a link to the NYS DOS on Apartment Hunting
You might also check with the hospital bulletin board and others working at the hospital.