Fortunately, Tokyo is also known for cheap 24 hours internet/manga cafes which allows you to stay there and kill time until the first trains start running again for as low as 500 JPY.

If you find yourself stingy and not worth spending a night at those overpriced Haneda hotels for just a night, a good option would be to take the Keikyuu Line to Kamata Station and spend a night at the 24 hour internet/manga cafe there: http://www.mangaland.co.jp/store.html?storeid=38

Overnight price between 22:00-08:00 only costs 500 JPY with free softdrinks, massage chairs, and 80Mbps high speed internet.