It has been a year since I went, but...here is what I remember:
Animal Kingdom Baby Care Center was very nice, large and clean. They have a big room with movies going and lots of space for kids to play. I don't remember any toys there, but there may be. Nice family restroom and baby change area. It is near Pizzafari. It is on the maps too.
MGM Studios baby care center is near the entrance at Guest Relations. It is very small. 2 small nursing rooms, 2 high chairs, changing area, no play area.
Magic Kingdom baby care center was closed for rehab when we were there.
Sorry, I can't remember much about the Epcot baby center either. I know they all have places to change baby, nursing rooms, supplies for sale, and an attendent there.
Maybe someone else can help more.