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I’m not sure if this is something that would interest you or fit your schedule, but here’s something we considered doing, so I’ll share my research.
Washington DC is about a four hour drive from NYC.
Many of the interesting museums, such as the Air and Space, Arts and Industry, and other Smithsonian attractions are open late this week.
There is a Days Inn that’s only 4-5 miles from the area the Smithsonian, White House, Washington Monument and other major DC attractions are located in.
The “Days Inn Washington DC Connecticut Ave” (Google it) only charges $59 per night, even less if you have triple-A.
This would be a very affordable family trip for a day or two.
The motel has free parking, a 4-sunburst rating (and is also rated highly on trip sites), and had a Metro (DC’s subway) station nearby, so you can easily travel to the tourist sites.
There are Kosher places to eat in DC, Silver Spring, and other nearby areas.