Hi Laurel,
welcome to LTH, it sounds like you have a good plan in mind. Are you thinking of trying more or less the same thing at various places, or are you more interested in getting different kinds of food at your stops?
I think, for myself (if I were planning a tour for an out of town visitor for example), I'd want to get different things at each stop for people to try. But then it would be hard to say that one place is "the best" -- as discussed in a separate thread on Vietnamese places, you might conclude that one place is the best for X and another is the best for Y.
If I were going to hit three places, driving around on the west side, I'd go to Sol de Mexico for carne asada with handmade tortillas (I think this is under their "small plates" section of the menu) and their sopecitos appetizer (chicken with mole poblano); to Cemitas Puebla for a cemita and a taco arabe; and Xni-Pec in Cicero for a taco of cochinita pibil and maybe an order of papadzules.
If I wanted to go to Pilsen, park once and walk around, I'd say goat tacos at Birrieria Reyes de Ocotlan; tacos de Sabinas at Nuevo Leon (grilled ribeye, beans, cheese in handmade flour tortillas); carnitas at Carnitas Uruapan or another of the carnitas places. Pick up a mini tres leches cake at Bombon for dessert!
Wow, I'm getting myself so hungry I may pass out. Unfortunately I am nowhere near any of the above mentioned spots...