People warn you that the Financial District dies at night. It's half true, and the half that's true is the good part. The offices empty out around six or seven, the lunch places pull their shutters, and by nine the streets around Wall Street are nearly yours. If you want a crowd, midtown is twenty minutes on the 4/5. If you want to walk narrow old streets with nobody in them and the towers lit above you, this is the only neighborhood in Manhattan that offers it.
What's actually open after dark is more than people expect. The waterfront works around the clock. The ferries run all night. The bars and restaurants that stay open are clustered in a few known places, mostly Stone Street, the Seaport, and the blocks around the Oculus, and everything below is a short walk from John Street.
One planning note: weeknights and weekends are different neighborhoods down here. Tuesday at 9 PM, Stone Street is calm and you'll get a table. Friday at 7 PM in warm weather, the whole block is standing room. Sunday, a lot of the lunch-driven spots don't open at all. Plan around the bankers, basically.
Here's what we send guests out to do after dinner, roughly in the order we'd do it ourselves.