Baylor University is a great free place to take a child to play. I have yet to explore the whole campus, but here are a few fun places to take children there.
THE BEAR PIT
Baylor's two live mascots (two female black bears) are kept in the Baylor Bear Pit, which is open to the public. The times I've been to see them they were sleeping--but still, you can't find a better free zoo exhibit. There is also a pretty river going by the pit.
THE FOUNTAINS by the SCIENCE BUILDING
There are two wonderful fountains connected by a man-made stream located between the Student Life Center and the Science building. When I first took my two year old to explore the campus, we stopped here and never got to the rest of it because he had so much fun splashing throwing stones in the little river.
While you're there, if you want to get out of the sun for a little while, take a trip through the first floor of the science building. The floors are made with stones that have real fossils in them, and at one end there is a cross-section of a giant tree dating past the time of Christ.
THE FOUNTAIN MALL
Ironically, there is no fountain located here, but it is a nice open space with some pretty landscaping where kids can run around.
There is lots of other places for kids to run around and explore (with adult supervision, of course). Just do be careful to park in visitor, not staff or student parking.