In all honesty, I don't recommend going out tonight and probably not tomorrow night either. It does not seem great outside and falling is embarassing.
BUT, if you forgot/willfully chose not to because eh, it's a hassle, to stock up before the storm, here's a list of what is confirmed open tonight and/or tomorrow in Jersey City.
UPDATED TUESDAY: Ok, so this blizzard didn't turn out to be a blizzard. It is still snowing outside, so hopefully you still get to enjoy a snow day. Jersey City is ready for you!