I'll be honest, I really like Shizuoka City. There may not be so many sights in the centre - Sengen-jinja shrine and Sunpu Castle Park are the main two - but it's friendly, compact, and a good place to use as a base to explore the sights and countryside around.
One place you might spend a very pleasant day (or half day if you rush) is the Mariko district, a quick drive or bus ride from the centre. Once you get away from the main road and flyover it's a very tranquil, leafy place, where you can enjoy strolling around slowly and taking in the peaceful atmosphere.
One of the main draws here is Togeppo Saioku-ji, a charming little Buddhist temple surrounded by bamboo, with an immaculately tended garden. Not far up the road is Kansho-in, another temple, where you're welcomed at the gate by a motley crew of statues in a whole range of oddball poses.
It's not all temples, though. The Sumpu Takumi Shuku is a fun craft centre where you can see displays of traditional local crafts and, if you have time, try your hand yourself at bamboo weaving, indigo dye or, less traditionally, sandblasting or laser etching.
From here there's a 'nature walk' over a forested hill. It's more strenuous and takes longer than following the busy main road, but it's also more peaceful and scenic, with some attractive views along the way, and an enjoyable hush all in the trees.
At the other end of the walk there's Seigan-ji, yes, another temple, where you can contemplate the pleasant grounds as you rest after climbing over the hill. Close by is the site of the Mariko morning market, held on 28th of each month, when you can find stands selling flowers and fresh vegetables from local growers.