24-hour food joints
Diner Grill, home of "The Slinger" - the motto of which is "Don't ask, just eat".
Basic, solid, diner fare in a spartan shell down the street from "The Long Room", a good place to get yourself in the condition that normally precedes a visit to a dive diner. I only order the Slinger when I'm extremely hung over; if I'm just hung over I typically opt for ham, eggs, and hashbrowns. Ham used to be sliced off the bone right in front but the city's inspectors have since quashed that practice.
1635 W. Irving Park Rd., Chicago
Tel: (773) 248-2030
The Long Room
1612 W Irving Park Rd
Chicago, IL 60613-2512
Phone: (773) 665-4500
1601 W North Ave @ Ashland
Takes me back to my youth hanging out at 2am in diners in New Jersey.
When I was there last time, I actually had a bowl of Manhattan clam chowder. Not superb, but decent and it hit the spot as well as the mark as far as diner food goes.
Standard selection of diner food from full dinners to burgers to sandwiches to the now ubiquitous nachos and burritos. And my favorite, french fries with brown gravy.
Parking lot next door is well-lit and there are security cameras that you can watch from inside the restaurant. (not that Wicker Park is super-sketchy, but it's not Smallville either).
Most 24 hour places are what they are... open and serving when others aren't so you sort of take what yoiu can get...
That said, The Golden Apple on Lincoln and George was my home away from home for ages. I used to live down the street from it for 15 years and worked as a Wrigleyville bartender--9PM to 2AM. By the time we closed and finished it was 3:30 in the morning and it just felt good to sit down. Odd how there were "regulars" at that hour, but cops, taxi drivers and industry people all hung there.
El Presidente on Ashland between Fullerton and Diversey. Not the best, not the worst, but when you want some Mexican or huevos post bar hopping, they are open.
Wacky? How 'bout Huck Finn's on Archer? Doughnuts, Ice Cream and diner food.
Further out on Archer, Mount Pindo's, daytime Curie HS hangout, late night diner. My dad's twin brother lived a block away, we ate there a lot as a kid... (not late night though!) Actually, I've stopped there a few times recently when the S/O's Midway flight's have been delayed.
EDIT... The Golden Apple Realty link is an error that won't delete!
Golden Apple Realty
4464 N Milwaukee Ave, Chicago, IL 60630
Golden Apple Restaurant
2971 N Lincoln Ave, Chicago, IL 60657
El Presidente Restaurant
2558 N Ashland Ave, Chicago, IL 60614
Huck Finn Donuts & Snack Shops
3414 S Archer Ave, Chicago, IL 60608
4955 S Pulaski Rd, Chicago, IL 60632
Hmmm, I miss the now defunct late late late late night greasy spoon Thai restaurant; River Kwai on Belmont across just east of Paulina. It wasn't the best Thai food in Chicago but it was the best at 4 in the morning after several beverages. This place had a strong following considering the hours and the dumpy decor. It was open from 10 pm to 6 am. I used to place my order at 2 or 3am and then hit the sack and wait for Moon's phone call. Yeah, Moon was always accomodating during those frigid winter nights. Anyone recall those 70's skin magazines behind the counter? Moon used to pass them whenever there was a long wait, which was always. I would love to hear more stories about River Kwai, the great late night food, and of course about the dynamic sister and two brother trio.
Meet with me off-line sometime. I'll tell you more than you would care to know about River Kwai.
Anyway, back on topic, my college pal, Dennis O'Brien, once put together a webpage which listed the various 24hr. establishments in Chicago. Dennis has since moved to the Bay Area, and his page is pretty outdated, but the OP might still find some use in it:
There are many more to add to that list, of course. A keyword search here at Chowhound should turn up a couple of threads, at least.