☆.A.
PPG Zoo & Aquarium www.pittsburghzoo.org
Carnegie Science Center & Sports Complex (totally awesome activities for a 3 yo!) www.carnegiesciencecenter.org
Carnegie Museum of Natural History www.carnegiemnh.org
Childrens' Museum of Pittsburgh www.pittsburghkids.org
You can head to North Park (giant park, lake, bikes for rent, etc.) to let him burn off steam, plus they have mini golf and batting cages at:
North Park Miniature Golf and Batting
840 East Ingomar Road
Allison Park, PA 15237
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Let me know if you need help with directions. Not sure what part of the city you're staying in.
Have fun!