Several stores in the U.S. carry this Icelandic brand—the local equivalent of North Face—renowned for its high-quality sports and leisure outerwear. If you forget to bring that warm parka or extra pair of gloves, head to the store on Bankastraeti, close to the 101 Hotel. Closed Sunday.

Refreshingly, Reykjavik isn’t overrun with international fashion retailers, but with the addition of this posh department store, Icelanders will have the chance to shop some of the world’s top fashion labels. Galleria Reykjavik’s carefully curated selection includes Chloe, Burberry, Loewe, Lanvin, Marc Jacobs and many other big fashion houses, and there is a section of the store devoted entirely to Icelandic designers. The space also features local art exhibitions and carries a line of luxury watches and home goods.

This store has a huge selection of the island’s ubiquitous wool knits, including sweaters, hats, gloves and little booties for children. There are two other locations in town, but this is the headquarters of the Handknitting Association, so you have a very knowledgeable staff on hand who are happy to talk about how the items are made and what makes Icelandic wool unique.

This sliver of a shoe boutique would make Carrie Bradshaw happy: the incredible variety ranges from sensible flats to ultra-fashionable stacked-plateau extravaganzas. Spanish cult brands Camper and Chie Mihara can also be found here. Kron is the sister store of KronKron, which specializes in fashion and accessories and is just down the street.

Run by the owners of Kron, this airy boutique offers a playful assortment of big-name designers—Sonya Rykiel, Vivienne Westwood, Marc Jacobs—mixed in with lesser-known finds like the loose-fitting dresses by Danish designer Henrik Vibskov and a selection of shoes and bags. Closed Sunday.

Cutting-edge Spaksmannsspjarir is a worthwhile stop for anyone interested in fashion and design. Launched by design duo Björg and Vala in 1993, the boutique is set up like an art gallery, with rows of white mannequins displaying the designs (there are only a few racks; most of what you want to try on has to be requested).

The combinations are original and daring: one ensemble might team up a classic knit cardigan with a massive tulle skirt and a double-strung leather belt; another might dress up a strapless gown with a purple cropped jacket and bold choker. There’s plenty of layering and lacing, and the clothes are decidedly sexy without being too revealing. It’s a great store to get ideas on how to combine and play with fashion. The impossible-to-pronounce name means “Wise Man’s Clothing.” Closed Sunday.