Every city has a 24 hour eatery where everyone ends up at one time or another.  LA just does it better.

The Original Pantry is best known for their cheap but good steaks and their great but cheap breakfasts.  My order of  ham and eggs with home fries, ranch toast and coffee came to all of $5.50

There's usually a line, but it moves pretty fast.  You can skip the line if you're willing to eat at the counter (worth it just for the show and the countermen's personalities) or sit at the community table.  There's also a line that is often shorter in the newer section.  But it's worth the wait to soak in the ambience of the original dining room.