May One
Clothing shops, a bookstore, a CD shop, a Muji (http://www.muji.net/eng/) top quality generic items, and an import store called Sony Plaza, among other things. There is a food court at the top and a high-quality grocery store in the basement.
ZaZa City
Amongst varied clothing shops, ZaZa City has a musical instrument store, a movie theater, a supermarket, a manga store, a video arcade, Toys'R'Us, Starbucks, MosBurger, Baskin Robbins, Uniqlo and more. The bookstore in the basement lever has a decent selection of English books.
Unagi Pie
If you need to buy omiyage from Hamamatsu to give to Japanese friends or co-workers, the typical gift here is called unagi pai うなぎパイ, or "eel pie". Actually more of a cookie made with eel bones, these individually-wrapped treats can be purchased at a store next to the south exit of the JR station, or at any number of pastry shops around town.
It is also possible to tour the factory where these are made, though it is necessary to make a reservation.
Shunkado 春華堂, Ookubo-cho 748-51 - Nishi-ku, ☎ 0120-210481, . edit
Entetsu Department Store
High quality clothing and other items. The basement contains a wonderful grocery and deli.
Shitoro Jusco
Hamamatsu has three of these somewhat western-style shopping malls. you'll have to catch a bus to these. the largest is in ichino-cho 市野町.
Plaza Mall Sago
There are a number of clothing shops on the first two floors of the Sago Hotel building on Yuraku-gai, including a used clothing store which sells clothes by the kilo-- good for the bargain traveler whose threads are wearing thin.
Sun Street Hamakita
This shopping center contains a bathhouse, a Toho Cinema, arcades, a food court, a 24-hour Seiyu, and dozens of clothing stores.