Portillo's on Ontario downtown serves up a variety of cheap eats like; Italian Beef, ribs, chicken, pizza, salad, hot dogs, etc.
REZA's is great for Persian/middle eastern cuisine. There's one on West Ontario downtown but I prefer the original location on Clark Street just north of Foster in the charming northside Andersonville nieghborhood. Try the lunch or weekend buffet/brunch.
Greek Islands at Adams and Halsted is excellent and very reasonably priced.
Thai Avenue at Broadway and Argyle for excellent Thai cuisine at dirt cheap prices.
TUFANO's VERNON PARK TAP at 1079 W. Vernon Park in the Little Italy neighborhood serves up mom and pop Italian food for dirt cheap prices. Cash only.
Wishbone on west Washington in Greektown for delicious Southern Cajun, and Mexican inspired breakfast & lunch.
Tempo Restuarant: for great fluffy ommlette's, greek dishes, and old standby breakfast items.
Original House of Pancakes on Bellview and Rush Street for excellent pancakes and apple pancakes.
Ina's on west Randolph for gourmet breakfast and lunch. Try the heavenly hots pancakes...the very best in the city!
Chicago Pizza Oven Grinder is a great cozy place for a different take on deep dish. Their single size pizzas come in a little ceramic bowl that they build the pizza in "backwards" and then flip over. Actually, i really don't go there for the pizzas, but really for the mediterranean flat bread and salads. they can be a meal in itself and its cheap!
Hot Doug's is great for really unique sausages (made with duck, lamb, elk, etc.) paired with interesting cheeses and mustards. Where else are you going to find a Thai spiced chicken sausage with peanut sauce on it? They have good regular dogs and polish sausages too. The regular dogs are only like $2 and the specialty ones are usually $6-8. Plus if you go on Friday or Saturday, they have fabulous duck fat french fries. The only problem is that it's difficult to get to on public transportation. If you are in to doing a comparison, you could try Hot Doug's, Wiener's Circle, and Superdawg.
Other than hot dogs, maybe Italian beef? Places to try could include Portillo's, Al's #1, and Mr. Beef.