There might be some 24-hour restaurants open near Shinbashi station as well. Not too familiar with the area, but I remember seeing some gyudon places (they serve other food also) like Yoshinoya/Matsuya around there, which are generally open 24-hours a day. There's a Tsutaya (bookstore/cafe) there as well, which is open late (2-3am). And I'm sure there are some izakaya, or places like Fuji Soba that are open late.

If you're not too tired, you can probably walk around a bit and find something. There's always the konbini option as well.