You will need a car for almost everything outside the downtown core — that is the bigger truth about Santa Rosa. Downtown itself, including Railroad Square and Old Courthouse Square, is walkable; the Schulz Museum, Luther Burbank Home, and the cemetery are all within twenty minutes' walk of each other and of the centre.
The CityBus network covers the rest of the urban area but is built for commuters rather than visitors. For the wineries and the coast, rent a car at the airport or downtown. Cycling along the Joe Rodota Trail (an old railroad converted into a paved path) is a pleasant way to reach Sebastopol; bike rental is available in Railroad Square.