I took my two teenage nieces to ESPN Zone two years ago. I thought that the food was terrible ... and so did the nieces. And to add insult to injury, it was very pricey for what you got.
My recommendations:
Chinatown
Frango Cafe or the Walnut Room in Marchall Field's
FoodLife in the Watertower plaza
Greektown
Little Village is also good for a walk.
Generally, teenagers are pretty happy to follow along and welcome different experiences - as long as there is plenty of food available.
Just took my "never eats spicy food" 13yo nephew to New Mexico three weeks ago. My sister in law called me last night asking that the phrase "red vs. green" meant.