With the large size of the Museum of Science and Industry, a stroller can be very helpful. The main limitation to bringing a stroller is the limited number of elevators. In the main section of the building, there are only two: in the red staircase and at the North end of the building (at the bottom of most building maps). This is particularly frustrating for getting up to the balcony, since they're a decent walk to several exhibits (take the red staircase elevator up to Flight and the North elevator for You! The Experience or the balcony level of Science Storms.
The museum generally has wide corridors, so even a double stroller is pretty easy to get around, with a few exceptions (the food court being the main one). I normally bring the stroller into the food court anyways, but even regular single strollers will have trouble fitting into the lines for food. I'll typically park the double stroller outside the line, ideally where the kids inside can see me pretty well. (Get to lunch by 11:30 to keep lines as short as possible.) With wide strollers, try the "extra seating" area through the doorway if it's open (see the Food page for more information) which has a little more space to navigate.
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