For the SW side (which is where Midway is at), as far as restaurants go, here are my suggestions:
Grand Duke’s, near 63rd and Harlem, for stick-to-the-ribs, quality Lithuanian fare. Lots of meat, potatoes, and dumplings here, with a European atmosphere (from the wooden decor to the beer list and waitresses.) One of my favorite places for comfort food.
Szalas, on Archer, east of Cicero. My go-to Polish food in this neck of the woods. There’s a little bit of kitsch to this restaurant, like the rope-pulled bell you have to ring to get in, and the interior decorations, which include a stuffed bear and a large sled, but don’t let that put you off. This place is legitimate, and attracts mostly Polish clientele. Another great place for comfort food. I’ve eaten a lot of Polish food in my life (my parents are both from the country), and I’ve found nothing that isn’t exceptional on their menu.
Vito & Nick’s Pizza on 84th and Pulaski. If you want Chicago-style thin crust pizza, this is my favorite place in all of the city. Order half special, and half beef & giardineira on your pizza if you want to try what are, in my opinion, their best offerings. It’s a cheap date, no fancy beers on tap. The interior of this place looks like its been frozen in time. Note, in particular, the carpeting on the walls.
This is a great area for Mexican, too. Birrieria Zaragoza is a Mexican goat place on 49th and Pulaski that constantly gets high praise for its goat dishes and made-to-order tortillas. According to Yelp reviews, it’s the second most highly rated restaurant in all of Chicago, right behind the wallet-busting molecular gastronomy gem Alinea. Even if you think you might not like goat, I’d give it a try. It’s nowhere near as gamey as you might expect. The goat is focus of this restaurant (there really isn’t anything else on the menu except maybe for a quesadilla), but those tortillas are also worth the trip. Hot, full of earthy corn flavor, and more crepe-like in consistency and thickness than the packaged tortillas you’re more likely familiar with.
There’s also good Mexican seafood down the street at 54th and Pulaski with Las Islas Marias. Zacastacos, a bit farther down at 59th and Pulaski, has my favorite grilled steak tacos, but also a deep-fried potato taco which is just the perfect interplay of textures and flavors. Kapeeko on 63rd and Pulaski is a relatively new Puerto Rican joint, and the closest place to you to try a lesser known Chicago culinary innovation: the jibaro/jibarito sandwich. Think cheesesteak with onions, lettuce, tomato, and sour cream, stuffed in between two flattened, garlicky planks of fried plantains. It’ll satisfy your caloric requirements for the rest of your stay, but worth a shot.
There’s plenty more, but that should give you some idea of what food, at least, is in your area.