Our first trip the baby was 12 weeks, we also had her almost 2 year old sister, almost 3 year old sister, and travled with a family that had a 17 week old, and an almost 2 year old.
We had a ball, the babies were great. I know both of us would wake up in the morning, do what we had to, and before we head to the park strap on the baby (sling, bjorn), and both the babies pretty much stayed there the whole trip. They were a breeze, actually all the kids were amazing!
We have very few pictures of them, lots of them in their carriers, but few of them because we wore them the whole time.
We rode almost every ride without a height limit, and most of them we did not even need to take baby out of carrier for. So, we would get in the ride, and just ride with the baby on us.
Actually that trip we did not hit the baby care centers, but two years later we went back and we had 2 two year olds, 2 four year olds, and a five year old, we hit the baby care centers then. But, remember they are there and they are nice, and air conditioned too.