Don't let us make you too nervous. NY is a great city, and you'll probably have a great time. It's quite safe, although until you know your way around, I wouldn't walk around at night alone. Most people are actually quite friendly towards tourists and will offer to help if you look lost. If you can, get over to see the Metropolitan Museum, and Central Park.
NY is an acquired taste. Try to get a feel for whether or not you want to spend 4 years there. If you have any interest in living there for a while, being a student is a great opportunity to do so, as it won't cost much more than going to school elsewhere, and both of those schools are really well situated in the city, as is Mt. Sinai as well. However, NY is not for everyone. It can take some getting used to. Everyone is in a hurry, they walk fast, and people will seem to be brusque and rude, but it's mostly that there's less time for small talk ( plus, they are brusque and rude ). It's crowded and noisy most of the time, although Central Park is wonderful on the weekends. So do try to walk around there if you can, and even spend an extra day there if you can ( Go downtown to the new World Trade Center, the aforementioned Metropolitan Museum, etc. ) You could see a lot in a day or two, and get a feel for whether or not you want to live there for med school. If you will have some extra time there, come back here and ask for suggestions on what to see, or PM me.
That said, I'm from NY, and lived and worked in Manhattan for 7 years, and I loved it. My whole family is still there, and my siblings live in Manhattan, but I wouldn't want to live there again.