Pittsburgh is really lucky to have such a world-class institution like the Carnegie Museums. The museum complex is so big, you will likely need more than one visit to see everything. I believe the Carnegie Museums rival the Smithsonian Museums in terms of quality of exhibits. Granted, the Smithsonian has the Hope Diamond. I really enjoyed the Carnegie's art section. Their dinosaur fossil exhibit is top-notch.
When I was visiting the Carnegie Museums this summer, they were hosting the Life On Mars international art exhibition. They showcased a very interesting array of international artists that were on the cutting edge.
A visit to the Carnegie Museums is a must if you're interested in either art or history and worth the admission price.