The Field Museum is huge, and you often need to walk a little ways from the car, so strollers can be wonderful. If you're bringing your own stroller, the east entrance (across from Shedd) is the only entrance without stairs. If you don't have your own stroller, you can rent them at any entrance for $3 for a single stroller or $5 for a double.
Strollers are allowed everywhere in the museum, except for ticketed special exhibits, where there is stroller parking just outside the exhibit (ticketed permanent exhibits do allow strollers, it's just the temporary ones that do not).
Many restrooms in the museum are small and difficult to navigate with a stroller. The bathrooms on the ground floor have the most space. My favorite is by the Explorer Cafe, but the bathrooms behind the Siragusa Center picnic area are good as well, and pretty empty except around lunch. On the main level and upper level the bathrooms do at least have a little space to leave a stroller outside (and I have brought the stroller into those, but I typically come close to tripping multiple people when I do so—it's not a big space).
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