Shizuoka City is something of an industrial centre, so has a number of business hotels clustered around the station to cater to business travelers. These are all perfectly good places (I expect, I haven't tried all of them), but if you're on a budget or want somewhere with more character, then Momotaro International House may hold more appeal. A cheap and cheerful hostel, it's further from the station but closer to the sights, and offers a friendly welcome.
It has rooms rather than dorms, but in every other way it fits the hostel image, with communal facilities and a certain lack of space. My bed was warm and comfortable, but took up a good 60% of the floor space in my room; that said, there was still room for a small fridge and a TV perched on a shelf over the foot of the bed.
Elsewhere there are shared kitchens, fridges, showers and toilets, and cosy lounges to hang out in and watch TV or chat with other guests and play some of the stock of board games. There's a separate floor for women guests, and a roof terrace that would be pleasant to sit up on in better weather than I had. If you need to be online there's free wifi throughout, and a free PC in the lounge if you're not carrying your own about with you.
The place is run only by "Total Manager" Shizuka, a bubbly, friendly hostess who lived for a year in Manchester. She speaks fluent English and has a wealth of local knowledge, from sights and transportation to what time of evening the local supermarket discounts its fresh deli produce.
It's really well located for sights, shopping and nightlife, though walking from the station might be tough if your luggage is bulky. It's just a few minutes' walk from Sunpu Castle Park and the observatory in the Prefectural Office tower, and not much further (but in the opposite direction) to beautiful Sengen-jinja shrine. There's a convenience store just up the road, and the Cenova shopping centre is just ten minutes' walk away, as is the main street of Gofukucho-dori, with its plentiful cafes, shops and restaurants.
All the rooms are very compact; she has singles for ¥3360 or bunk-bed twins for ¥5250, making them pretty much the cheapest rooms in town! So for a cheap'n'cheerful place to stay, Momotaro International House is a good choice.