Henry Clay Frick's mansion, Clayton, is a must on any tour of Pittsburgh. The center's grounds include an art and car museum, working greenhouse, a great cafe, and of course, the mansion itself.
You will be blown away by the woodwork in Clayton--it is nothing short of amazing. The furnishings, decorations are also exquisite and original to the house. A tour of the home takes a full hour and gives you a view into the life and times of one of Pittsburgh's most loved (or despised).
If you are short on time, I would recommend prioritizing A visit to Clayton and then to the other structures at the center. There is simply no comparison to Clayton.