I've only been in the one in the MK and there is a small room with some chairs and a tv where she could walk around for a minute or so!
Your best bet is to look for the play areas during less busy times... I don't know when you're traveling but I found that later in the day the play areas weren't as crowded. My 14 month old had just learned to walk on our first trip and I was afraid to let her out b/c she would get trampled in a second! Pooh's playful spot was nice in the evening. Another great area is inside the living seas when it's not too busy... I let her walk around and touch the glass to the tanks. Another cute area is the one under splash mountain (can't remember the name of it) but my daughter had a lot of fun there during EMH one night! I would suggest you avoid the big play areas in DHS and AK - they're too crazy for a young child! My kids love 'em now but they're 5 and 2 years old!
Here's another little tip. When at AK we usually head straight for the Safari and get a fastpass. While waiting for our return time we walk the Pangani Forest trail (spelling?). First thing in the morning it's not busy at all and I let my children take their time and walk the trail at a leisurely pace. It's a great place for them to stretch their legs before the crowds show up!