As soon as you step away from the urinal at the beginning, type "DNCLIP" to turn on noclip, face down, and move down through the floor. You'll immediately see a piece of cityscape way below you. Continue heading down for a few minutes, and eventually you'll find yourself floating above a Vegas style strip. As you keep going down, down, down, eventually you're going to see a gray wall, with some helicopters and jets floating in nothingness. (By this point you're clearly a few hundred feet above the city, with tall buildings and the Fellatio club nearby.) In this wall, between two golden statues, is a window. Pass through it to get into Duke's room, the one where the Holsom twins are at the end of the first demo level. Things are interactive in here.
I'll spoil the rest for those who want to look around by themselves.
You can play pool and turn a bunch of lights on and off. If you turn around the window will show a view of the area with a big alien spaceship above it. Walking across a certain area of the room will trigger the helicopters and planes for a flyby of the window. The TV in the room with the girls is going to be cycling through some channels - a news break with headlines scrolling at the bottom, a Holsom twins music video (from their album called Full House, real subtle guys) and a clip from a late night talk show called Too Damn Late starring Jimmy O'Lenoman. (You should be ashamed of yourselves, Gearbox.)
One fun spot is the bathroom, where you can walk in and admire yourself in a mirror, and get several lines of dialogue from Duke about how awesome he is. There's also a phone on the wall by the toilet, where somebody left a message.
The Holsom twins are stuck on their knees in front of the couch in the TV room, waiting for you to trigger the end of your boss fight. You can see the controller floating in midair. Turning off one of the light switches in the suite, however, will actually activate the twins, where they'll giggle about being scared of the dark or something similar. Afterwards, walking up to them will trigger some dialogue. Walking out of the room and down the hall, you can see a hallway with pictures of Duke doing awesome things, and then an elevator. Going into the elevator and using the buttons (guess what number floor Duke lives on) will send the elevator down, save a checkpoint and attempt to load the next area. Since it's just a demo, and the data isn't there, you'll just get a blank screen.
Quit to the main menu, then try to load that save and you'll get a message saying the game was saved in downloadable content that isn't installed, and to reinstall the purchased DLC to continue. Did Gearbox announce plans for single player DLC levels yet?