Harry Caray's is my favorite restaurant at the Chicago Midway airport. It is the only place that serves remotely interesting vegan meals.
The vegan options that I've seen include spaghetti (with either the marinara sauce or topped with garlic and oil), bruschetta, mixed green salad, Tuscan salad (contains mixed greens, hearts of palm, artichoke hearts, tomatoes, roasted red peppers, bermuda onions, garbanzo beans, cucumbers and fresh mozzarella with Balsamic vinaigrette - just ask them to hold the mozzarella if you're vegan).
I usually get the garlic and oil spaghetti or the Tuscan salad. Both are really tasty and filling. Harry Caray's is a great place to eat if you have at least 45 minutes to kill before boarding your plane. If you have 30 minutes or less, they can still accommodate you but you have to eat at the bar and can only order a salad or sandwich.