This one is worth the drive for the best homestyle Mexican food in the area. Absolutely fabulous. Very simple - a basic cafe in the back of a little grocery. Try the carne desebrada, the asada, the burritos, the tacos. The Tey's breakfast absolutely rocks, and on a dreary afternoon the caldo (entree-sized soup) will give you the strength to go on. Don't expect them to speak English - just point at the menu and smile.
Tey's Grocery
5400 W 31st St
Cicero, IL 60804
Look it up on Yelp for directions etc. (It's actually easy to get there - take Ogden west, or take the 55 to Central, go north 1 mile to 31st, turn right, go a couple blocks. From the time you hit the 55 out of downtown, it's 15 mins max. At lunchtime, anyway.)