My kids love the DAI!.
We discovered the children's experience center at DAI over the winter and have been back several times since. My four year old twins love it there! The area is contained and not far from the bathroom which is always a plus. Lots of hands on stuff and it changes pretty often too.
I don't know exactly when they started the free admission, but it's a great deal! The building is beautiful and fun to explore all the galleries. The setting on the river with a great view of downtown is nice too.