Xni-Pec isn't terribly far either. Just a straight shot up Cicero, left on 24th Place (just after the overpass. You can take the overpass, but it's a bit confusing). Go a block west on 24th place (the first left you come to after the Ogden overpass), turn south on 49th Ave., turn right on 25th Street, and go down to Laramie and it'll be on your left, about two doors down from Laramie.
Xni-Pec
5135 W 25th St
(between 51st Ave & Laramie Ave)
Cicero, IL 60804
Also near Midway is one of the outposts of Las Islas Marias, if you're in the mood for Mexican Seafood.
Las Islas Marias
5401 S Pulaski Road
Chicago, IL 60632
(773) 767-0908
as well as a wonderful birrieria, Birrieria Zaragoza
Birrieria Zaragoza
4852 S Pulaski Rd
Chicago, IL 60632
(773) 523-3700
So, Yucatecan cuisine, Mexican seafood, or goat specialties, take your pick. edit: I should add that while I give all of the above high marks for food, I'm not sure I would necessarily call any of them particularly exemplary in terms of ambience.