I have written several tips about things to see and places to visit in the downtown area, but I figure I might as well also simply suggest exploring downtown. It consists basically of two parts separated by the freeway, Hwy 101: the main downtown area around Old Courthouse Square east of 101. This is the historical core of town, where most of the businesses, offices, biggest buildings, restaurants, etc., are located. It is also the most office-oriented portion and has more modern buildings. Bounded by College Ave in the north, Sonoma Ave. in the south, and Brookwood Ave in the east, its core is Old Courthouse Square and 4th St. Railroad Square is the portion west of 101 near the railroad stations. It is the more old-fashioned area and generally has smaller buildings, fewer offices, and a higher concentration of restaurants and antique shops. One can walk underneath the freeway to get from one to the other, but the giant brick mall, Santa Rosa Plaza, is between them and one must either go through it or go around it at 1st St or 6th and 7th Sts.
The websites for Downtown in general and Old Courthouse Square have more info on downtown as do my other tips. I mention Railroad Square and its website in a specific separate tip as well.
Santa Rosa's Downtown is home to hundreds of stores of all kinds, anchored by a mall called the Santa Rosa Plaza, but also offering a variety of traditional street shopping.
Courthouse Square is named after the park and gardens around the courthouse and includes some 800 retail shops and restaurants. This area also features the town's Wednesday Night Market and seasonal events. Interestingly, there is no longer a courthouse in Courthouse Square as the Sonoma county Courthouse was destroyed in the 1906 San Francisco Earthquake.
Railroad Square is named after the historic 1904 railroad station. Other historic buildings in the area include the warehouse and the Railway Express Agency Building, both from 1915, the Hotel LaRosa which was built in 1907, and the Western Hotel from 1903. Railroad Square is now a major shopping destination in Santa Rosa with antiques, furniture stores, jewelry stores, a theater, and about 10 restaurants.