I hate to advocate drugs, alcohol, violence, or insanity to anyone, but they've always worked for me.
The Blue Light is on Western a little North of Belmont. It is fantastically sleazy. They have a late license and open at 7 every morning. It's the kind of place that looks like you'll get beat up in there, but you won't (unless you ask for it, in which case, please stay out).
Hipsters are discovering it, so go now before it's too late, even if you yourself are a hipster. For now, it's always possible to find a spot to sit, even at 2:30 when all the other late night places are packed. You may have to walk to the back room, though.
It's a good place to go after Hungry Brain (2319 W. Belmont) closes at 2, when you're not done drinking.