Chowpups visiting Chicago
Greek Islands at Adams and Halsted for amazing food, free parking, and reasonable prices.
Raw Bar in Wrigleyville on Clark Street is fantastic and way underrated! Persian and Egyptian spiced steak, seafood, and chicken etc. Very extensive menu and cool atmosphere.
Reza's (there are several locations but the best is the original on Clark Street in Andersonville) in Andersonville for very good middle eastern food in a fun neighborhood. Check out the Hop Leaf afterwards for a wide array of Belgian and other European brews.
Al Kaayam at Kedzie at Lawrence for great and cheap middleastern food. Great Shawerma.
Ethiopian Diamond is supposedly great. On Broadway in Edgewater.
Pancho Pistolas for the very best Mexican Skirt Steak and much more for dirt cheap prices. In our Mayor's former neighborhood close to US Cellular/Sox Park 700 W. 31st Street at Union and Halsted. Modern exposed brick decor/clean space/nice atmosphere.
Andalous Moroccan in Wrigleyville on Clark street for great Moroccan Food, dirt cheap prices, and BYOB (bring your own booze).
El Llano on Lincoln Avenue just south of Irving, at Damen for dirt cheap tasty Columbian Churrasco Style Steak and Chicken. I prefer Las Tablas on Lincoln south of Belmont Avenue but it's a few more dollars per entree.
Oak Park has pretty good access to public transportation. Taking the blue-line train to halstead then walking North, will get you to Greektown. The focal point for Vietnamese is Argyle street, which is right next to the red-line train (you can transfer to that downtown from the blue-line or green-line). As to middle-eastern, there are actually a couple of restaurants in Oak Park (Jerusalem and Grape Leaves), but I don't know much about them, or if they still exist. Although there are middle-eastern restaurants throughout the city, the greatest concentration is probably near the Kedzie stop on the Brown line.
Greek - Greektown! Halsted b/w Van Buren and Randolph. Most of the restaurants are good, with big portions and very reasonably priced. My favorite is Parthenon.
Middle Eastern - If they are going to Second City or want something closer to downtown, Old Jerusalem (Wells north of Schiller) is great.
Chicago has over 7000 restaurants, 2/3 of which probably fall into the serious but cheap ethnic category. It would help to know where they will be staying and what kind of "ethnic" food they are interested in. The main categories represented here are regional Mexican, Latin/South American, Caribbean, African, Indian, Pakistani, Middle-Eastern, Vietnamese, Korean, Thai, Greek and Eastern European.
The best thing to do is get a CTA pass and go out and explore the neighborhoods. For instance, within a mile of my house there are restaurants with cuisine from 5 different parts of Mexico, Jamaica, Belize, Ethiopia, Erritrea, Nigeria, Peru, Colombia, Cuba, Persia, Assyria, Viet Nam, Bosnia, Croatia, Greece and Korea. And my neighborhood isn't even considered a dining destination.
Devon Ave, Argyle Street and the Maxwell street Market are probably good places to start.