There were state-owned clothing/cosmetics shops. Photographer Ilya Varlamov published some old photos of them here. First, second and third photos are right up your alley. Some commenters complain about low quality of goods ("my boots didn't survive the first winter!"), others have warmer memories about them ("these stewed fruit juices were cheap and tasty!")

You could also order individualized clothing in special "ateliers" - state-owned enterprises which employed tailors. This article, in Russian, nostalgically remembers one such atelier in a small Ural town, describing how popular the tailor Galina Iosifovna was among local women (they were willing to wait for quite a long time in order to ensure that she, not other tailors, would be the one who sewed their order), and how the fall of the USSR forced its employees to find informal sewing and tailoring work.

There were Soviet fashion magazines. General "home labor" magazines also published materials on clothing. This article, also in Russian, describes the post-war creation of centrally-governed design studios all over the USSR. These designers, according to the article, saw their mission as creating "elegant, practical and hygienic clothing that takes into account Western fashion tendencies, but doesn't slavishly copy them", often integrating folk motives to make their clothing unique. However, the demand for quick and fast mass production often overrode all other considerations, as Soviet press itself acknowledged on occasion. A 1970 Soviet book about industry noted that "this system suppresses the idea of artistic creativity, making the very idea of design overly utilitarian".