While not a travel situation per se (only 3 miles away, lol) we wanted to share our experience. The American Museum of Natural History, offers a sleep over a few times a year, get on their email notification list it sells out fast. We booked last August for January 6th.
Limited to about 500 people, each child needa a parent along, but its a blast. Basically the Museum is only open to those with reservations, not complete access but maybe 60%. There are activities like, flashlight fossil hunt, live animal presentation anf an Imax movie. Sleep under the big blue whale on cots, whils not for everyone we loved it.
Overall if you children love science and natural history its a great night, sorry no Ben Stiller