I brought a baby or two to BGW some years ago. (They were mine, to be clear.)
The basics probably haven't changed too much since then. I recall widely available changing tables; the rugged terrain providing a fantastic accidental workout (either pushing a stroller or carrying the little one long distances); a surprising preponderance of other people also with strollers, which was reassuring when I was pushing one and annoying at all other times; the vague sense of dread before confirming whether folding strollers were either permitted or forbidden on the sky ride or the train; appreciation for any food that can be eaten with just one hand; tremendous appreciation for the park's tendency to allow baby-focused snacks, food, and water in at the gate; and a newfound affinity for finding every shady or air conditioned out-of-the-way space in every corner of the park.
Perhaps the single biggest factor in enjoying the day was the prevailing temperature. If below perhaps 95F, it was a pretty good time spent appreciating the park in a new, slower way. But one day it was just shy of 100F, and while I would have been fine otherwise, the rigors of pushing/carrying Li'l Halfabee #2 around all day in that heat and humidity were enough to send us home before mid-afternoon. Your choice to visit in the spring is IMO a good one from at least a temperature standpoint.
Beware:
- The Sesame Street Forest of Fun area is neither a shade-producing forest of any kind, nor, for truly little ones, very much fun. The untamed vigor of four- to nine-year-olds blithely cartwheeling and sprinting through the water play area makes it a no-go for early toddlers with parents possessing any rudimentary sustenance-level protective sensibility. On the other hand, babies do tend to love the character stage show a short distance away from the water play area. Li'l Halfabee #2's first words of affection were not "Mom" or "Dad" or "Li'l Halfabee #1," but rather "I love you Big Bird." It was also their first complete sentence. That is a true story, exactly as quoted. (FML.) So mind the tiny ones carefully around the edges of the fountains, and catch the song-and-dance revue on the elevated stage for their sake. Otherwise they may not learn how to love. And as their parent it will be your stupid fault just like everything else.
- The hills do not discriminate in their gravitational cruelty. With kids now fully ambulatory, I saved a mom-stranger's baby in a stroller from rolling, runaway-train style, down the entrance path toward the log ride while mom-stranger stared at her phone, facing the other way, apparently oblivious. I am 85% sure nobody else could have caught that rocketing pram before it disappeared down the lane and eventually careened into something, absent the jump I got on it. Pat on the back for me I guess -- usually it's the dads that are characterized as oblivious, fairly or not -- but more importantly, don't trust stroller brakes or "It's not rolling now; I'll just look away for a few moments" in a hilly environment like BGW.
- Holding your baby while on the sky ride can be unsettling. Your own personal center of mass is obviously lower than the wall of the vehicle, making it exceptionally difficult for you to fall out. And baby's center of mass is... maybe lower than the wall of the vehicle? Maybe not? Maybe you want to hold baby just a bit lower, below your neck-shoulder area instead, but now they are squirming and you aren't sure this is any better? Same goes for the train: there's just nothing between baby and falling out, except your diligence and the hope of sitting in the center of the row. If you are the type to drive over a large bridge and worry about accidentally yanking the wheel during a sneeze and inadvertently crashing the car right through the concrete wall at a previously unknown weak point and plummeting 200 feet to a watery grave -- damn the odds, it could theoretically happen -- you will feel the same way with a baby on the sky ride. I'm not the type to worry about such things, but you might be, especially after reading this.
Overall, I'm glad I brought a baby to BGW, and would do it again if I had any more babies sitting around. My kid, on the other hand, doesn't remember or care,
at all, or so they claim, which gives me slight pause and leads me to wonder whether perhaps it was all just an infant's ploy to get conveyed around a pleasant park all day for free and then hit on Big Bird. But it was worth it to me, and that's all that matters.