Since your child is only two I would not suggest Pump it Up--if it is full of big kids your little one might just end up being run over.
Woodland Hills Mall has a great contained and free play area (and it is air conditioned). Promenade Mall has one too, but it is a little smaller.
There is a splash pad at Hunter Park on 91st between Sheridan and Yale. And I think that there used to be a splash pad at the park outside of the zoo. There is also a play fountain at the Riverwalk in Jenks (near the aquarium).
There is a new children's museum called Kalidescope at 61st and Sheridan (I haven't been myself).
LaFortune Park has a great play area that is mostly shaded by lots of trees. It is on Yale between 51st and 61st.
I hope that some of these suggestions help.