I always loved bringing my babies to the zoo. Whether it was with my first baby or bringing baby along with older siblings, the zoo was where we started: lots of walking, great exhibits that I and older siblings enjoy seeing, and nobody around me batting an eye would baby would lose it and cry or scream (plus lots of open space for when that happened).
At about 7 months I noticed my children being able to follow big animals moving around; before that it's really about being outside, having good topics to talk to baby about, and having fun stuff for the older people, whether they are bigger kids or adults. Before 7 months, I just went wherever I (or the big kids) wanted to go and brought baby along. Tropic World (with primates) is the only really popular space that doesn't allow strollers, although I've broken that rule once or twice when the zoo isn't busy. Even after 7 months old, I mostly went by what I or big kids wanted, but I would be more likely to include rhinos, giraffes, and dolphins since I thought they were easier to watch.
The main rule I had for older siblings was that they had to remain within eyeshot of me. Once I was comfortable they could follow that rule, the zoo was as easy an outing as there was (which isn't to say I didn't leave it exhausted, but it was more enjoyable experience along the way!).
One challenge is when babies are big enough to want to get out and crawl around: there's not a lot of space outside that doesn't have either lots of people running through or a fair amount of goose poop all over. I've risked the goose poop to have kids crawl around in the west mall (the open area to the west of the fountain), though be wary of the feisty geese in general, especially when there are baby goslings about. The Play Zoo has lots of good areas for babies to be on the floor, including the Animal Hospital, plus an area in the back especially for non-walkers (though if you have older kids, the crawl area in the back doesn't have much for them to do nearby).
I strongly recommend BZ Red Hots if you're getting food at the zoo. The other main restaurant, Cafe del Sol, is the only other place with high chairs, but it doesn't allow strollers inside. At BZ Red Hots, you may bring a stroller in (although it can be difficult to navigate when it's even a little busy), plus you order and then are called up when food is ready. I often order and then get kids situated at a table, so that I can return with both hands free when my number is called to get the food. At BZ Red Hots, the high chairs are tucked around corners on two sides: go around either wall that the soda fountains are on to find them.
See more information about food here.
Brookfield Zoo publicly encourages nursing wherever you feel comfortable doing so.
If you want privacy, there is a nursing room in the Play Zoo (which is by the south entrance). At the entrance, say that you're going to use the nursing room and you (and kids) will be admitted for free. Go all the way to the back and there is a room to the left with a nursing room inside. There are often volunteers in that area that can help direct you if you can't find it.
On the west side of the zoo, my favorite area is a small dead-end path just to the east of the giraffes. There's low foot traffic, and adults and bigger kids can watch the giraffes or run around a little on the path. On the east side, the underwater dolphin viewing is a little busier but decently calm, a little dark, and has fun things to watch plus good space for bigger kids to run around.
If there are older siblings, the two playgrounds are good choices to provide entertainment while nursing. There are benches all over near both and while there's not as much privacy, there's a good chance others will be nursing there as well. The two playgrounds are east of the fountain (go towards BZ Red Hots and it will be on your left) and on the west side, just south of the bison.
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