As a proud upper, upper Manhattan resident, I would argue that it's super safe, i.e. as safe as any major city gets in the lovely USA. Also, LOL @ "walk-up."😀 I don't know any of my friends in Brooklyn with elevators. Walking is NYC life, up, down, and sideways. But Brooklyn is great, very nice housing deals to be had on decent places, especially if you have roommates and split a carved-up 2 or 3 bed. What you will not get is space. Your room with be a closet, but you'll be happy.
And, you'll probably want to live very close to campus for the 1st year. Commuting from where I live to Downstate is about 1.5 hours on a good day. So, better not to stress about which trains are working that day.
Good luck to those interviewing, probably see some of you there!