Although NYC as a variety of master's programs in biology and health related disciplines, it seems to me it really does not have any special masters similar to Georgetown.
Hunter offers masters in Biology as well as Biochemistry. The core courses are offered in the evening. Since they are lecture courses they do not close out. (There are also research opportunities.) As long as one has taken the GREs & as a reasonable science background, you can take them as a non-matric. Hunter also offers a master's in phar research based at Mt. Siani. Many people take these courses to enhance their Med scholl applications.
Although one can do some good learning in these programs that will help you, I think there is nothing quite like a Georgetown-like smp designed to get people into Med School.