They have updated the Nintendo store, that might be a good option.
There is the MTA (transit) museum in Brooklyn that had a lot of kids in it.
Coney Island might be less cold by mid April? I do recommend using the bathroom before and after Coney Island, you do not want to use those public toilets
There is a pinball arcade in midtown where you play by the hour, not sure how much your kids would like it though.
There is the Intrepid museum on the west side, lots of planes on top, a version of the space shuttle and other stuff inside.