When lower Manhattan flooded last winter, the systems behind the exchanges were just fine. None of them are actually in Manhattan. (The big NASDAQ billboard at Times Square is just advertising. There is no NASDAQ facility at that location.) NASDAQ doesn't even have a trading floor. NYSE/Euronext was prepared to shift trading control to Chicago, where they also own Arca, another exchange.
The Wall Street firms panicked at the plan for trading going on without them. They demanded that the exchanges be shut down until the firms could get back up. That was done.