Sonoma County Museum, Santa Rosa
The Sonoma County Museum is in the old Post Office. It is worth visiting for the building itself, which is gorgeous inside and out (and, for those familiar with Turkey, kind of resembles some neo-Ottoman architecture seen from the late empire and early Republic). Designed in 1908 by James Knox Taylor and completed in 1910, it is one of the oldest Federal buildings in the state and one of the area's most significant landmarks.
Part history museum and part art museum, it also has interesting exhibits on the history of the area and art. It has permanent displays on the history of Sonoma County, although the emphasis tends to be Santa Rosa and the displays rotate. These include rotating displays covering a range of things such as the history of the mapping of the California coast and the impact of the 18 April 1906 earthquake on the area. Other displays include woodworking art, the art of the pottery of Marguerite Wildenhain from nearby Guerneville (just NW of Santa Rosa) and Edith Heath and Heath Ceramics in nearby Marin County.
There is also a permanent collection on the works of Christo and Jeanne-Claude with some of their art pieces having been donated to the museum. It also has an emphasis on the Running Fence which in the 1970s ran through farmland in northern Marin County and Southern Sonoma County and ended up at Bodega Bay (I remember seeing part of this as a kid when we would drive to Bodega Bay and wondered why fences were covered in white sheets).