Here's a few of my favorites:
Pizza:
Louisa's, Crestwood. Similar in style to Lou’s.
Nick & Vito's, Chicago. Get thin crust.
Barraco's, Evergreen Park
Nino’s Pizza, Alsip
Beef
Pop's, Palos Heights. I think this one is much better than the one on Kedzie.
Hot Dogs and Burgers
Willie's Weenie Wagon, Markham. Try a Coney Dog.
Janson's, Chicago. Good shakes and decent dogs.
Nicky's, Crestwood. There are a lot of these grease joints around here—this is my favorite.
Wojo's, Evergreen Park. A million shakes and burgers.
Top Notch, Chicago.
Wonderburger Grill, Chicago. Small local burger joint.
Chinese
Chi Tung, Evergreen Park
Sesame Inn, Evergreen Park
As far as I know, these two are as good as it gets around here for Chinese. If you don't like these, you're gonna have to drive a little further North.
Mexican
Atotonilco, Worth
Chains
Because of the lack of variety, these chain restaurants are often necessary.
Lindy’s Chili, Chicago
Leona’s, Chicago
Potbelly’s, Oak Lawn
Nancy’s, Alsip
Rosati’s, Chicago
Portillo's, Crestwood & Oak Lawn
Mr. Sub, Alsip
All of the “Chicago” locations are right by Beverly.
If anyone has any others suggestions, please, please continue to post them.