I don't think I'd sleep. I would just spend the night wandering around Epcot and spending time in some of my favorite spots. I'd walk around Future World and enjoy the light-up sidewalks. There's something about those sidewalks that make me want to twirl and skip and jump. I've never done it because I'd look like a weirdo but I'd do it I were stuck in Epcot overnight.
Then I'd go over to World Showcase and spend time in my favorite pavilions. I'd have a margarita in Mexico, hang out in that little fishing village at the end of Maelstrom, talk a walk around the UK pavilion and talk to whoever is with me in my silly, fake English accent, sit at one of the tables by the bakery in France and read a book, and sit by the fountain in Morocco. If there was time, I'd spend time in the other pavilions, too.
But if I had to sleep, I think it'd be in the little fishing village in Maelstrom. It really is one of my favorite spots in Epcot.