I find Hollywood's food to be oversalted.
There is Bongo Room on Milwaukee, but in my opinion their food is just ok and not worth the hype. as well there is Toast on Damen just north of North ave. I haven't been there in a while, but they always used to have really great stuffed french toasts.
A couple of nicer sit down places not too far from there are Flo's at 1434 W. Chicago Ave and Hillary's Urban Eatery (hue) at 1500 W. Division (Division and Greenview). both of these places have really good and creative breakfasts.
I also really like Bialy Cafe at Chicago Ave and Noble for inexpensive and tasty omelettes and other simple breakfast dishes.
and a little further west are Flying Saucer Cafe at Division and California, and Mama Kitty's at North and Kedzie. Flying Saucer is more of a hipster spot, but inexpensive and good food, and Mama Kitty's is straight up diner/greasy spoon where you can get breakfast with coffee and tax included for about 5 or six bucks.
Leesh