There's a GUM former Kunst&Albers department store on Svetlanskaya, across from Ploschad Bortsov Revolutsii, and electronic stores further east that can help with power converters and the like.
Local markets are spread throughout Vladivostok and provide the basic groceries for a neighborhood. Some even have a butcher but most all provide sausages and frozen meat. Larger markets sell clothing, shoes, and everything else imaginable in addition to food.
Sportivnaya Market is the largest market in Vladivostok. Its maze-like warrens are full of people selling most everything. There is a large Chinese presence here, and knockoffs and Chinese imports abound. The range of food sold at this market is fabulous but is probably a bit unusual for everyday fare.
Mir Pryazhi
A nice place to buy local crafts handmade jewellery, knitwear, porcelain beads. The shop also sells yarn and handcraft items.