My mom works for Davison Design and Development, which is connected with Inventionland. Unless you're with a Girl Scout troop (or something similar) or you're planning to design a product with them, I'm pretty sure you can't get a tour. But things might have changed.
Definitely visit Primanti's, it's wonderful. Shadyside is cute, it's not too far from Downtown. Check online for top lists of places to eat downtown. There are a lot of neat places to eat in the city, but they're usually spread out.
Hit the Strip District early! The Strip's shops (most of them, anyway,) start to close around 2 to 4pm. There a lot of different and unique shops in the Strip. I'm not sure if Peace, Love, and Little Donuts is still there, but the donuts are wonderful. DeLuca's is great, but so is Pamela's. Just be prepared for the fact that a lot of the restaurants in the Strip only take cash.
The South Side is definitely fun! It also has some cute shops and restaurants.
The Zoo and the Aquarium are in the same place, so it's a matter of choosing to visit the aquarium than paying extra for it. The last time I went, it was all one price.