I agree w/likepgh -- Phipps is a lifesaver in winter!
Center for Creative Play is great for burning energy but don't forget the Toy Lending Library (
pittsburgh toy lending library), which is also fun and very laid back, and right in Shadyside.
The Carnegie Libraries also have lots of different storytimes (
Don't Miss This! Carnegie Library of Pittsburgh) that might be an option. A perfect day for me might mean going to a storytime at the beautiful new library in Squirrel Hill and treating my kids to fancy cupcakes at Dozen (
Dozen cupcakes Pittsburgh | welcome).