The official state history museum, on a hilltop across the road from the Capitol. The exhibits cover everything from the pre-contact Native American peoples through the Land Runs of the 1880s and 90s, the Dust Bowl, the oil boom, and the civil-rights era. Outside there is a small collection of oil derricks and a single-engine biplane, both useful reminders of the things Oklahoma has been good at.
Underrated and rarely crowded. The Dust Bowl gallery and the surprisingly frank treatment of the 1921 Tulsa race massacre are the strongest parts. Two hours easily; longer if you read the captions.