The centre of Shizuoka city may be compact, and may not have all that many sights, but I still wouldn't want to walk between all of them. Fortunately, I don't have to: leaving from the north exit of Shizuoka station, the Sunpu Roman Bus does a loop around the centre, stopping off at many of the sights. There are two routes of roughly six kilometres each, one for weekdays and one for weekends and holidays, and the bus covers them in around 40 minutes on its way back round to the station.
"Sunpu Roman Bus"? Sunpu is the historical name for the Shizuoka city area, and Tokugawa Ieyasu lived in Sunpu Castle, the ruins of which you can find in Sunpu Castle Park. "Roman" I guess is short for 'romantic' - think Holiday, not Empire - which makes more sense when you actually see the bus. According to the Shizuoka City Government website, the bus is modeled after the Orient Express train, and its handsome, colourful old-fashioned livery certainly does catch the eye as it pootles around the town.
As well as the park, the bus stops at Shizuoka Sengen Shrine, the city's main sight, which would take about thirty or forty minutes to reach from the station if you walked it. It's a handsome, sprawling shinto shrine with lively, colourful carvings, a peaceful garden, and a forested hill to the rear where you might spot wild boar snuffling around.
Other stops include: Cenova shopping centre, which is also home to Shin-Shizuoka station, terminal of the Shizutetsu railway line; Keyo-in temple, a small but pleasant Buddhist temple not far from the station; and the Prefectural Office Tower, which has a 21st-floor observatory giving a fine view over the city and surrounding countryside.
Buses leave every half hour between 10:00am and 6:00pm from stand 10 at the north exit of JR Shizuoka station. A single ride costs ¥100 for adults or ¥50 for children of elementary school age.