another Pittsburger here!
Here are some things I would consider must-do's:
Kennywood (get discounted tickets at our local grocery store Giant Eagle & save like $10/ticket)
Pittsburgh Zoo (it's so awesome) If you have Phila zoo passes, I believe our zoo is reciprocal
Carnegie Science Center, a bit expensive but it's great! Check out a flick @ the Omnimax Theater
Strip District on a Saturday morning (it's like a street-market) bring cash!
Idlewild is great for kids, it's actually the #2 best kids park in the world. It's about an hour outside of Pittsburgh.
Take a walk along the North Shore and let the kids play in the water features, and look at all the stadiums, and eat @ some good restaurants.
National Aviary is nice, but it gets really hot and smelly in the summer (IMO)
A couple of our county parks (South Park, Settlers Cabin) actually have Wave Pools and it's only like $4/person to get in.
Sandcastle is fun too, but buy tickets online as they're cheaper
hmm... If I think of more I'll post!