Shopping Centres:

1. Kringlan Shopping Mall - Reykjavik's largest shopping mall with over 150 stores, offering a wide variety of fashion, home goods, electronics, and more.

2. Smáralind Shopping Center - Another popular mall, featuring both international and local brands, along with a diverse selection of restaurants and cafés.

Markets:

1. Reykjavik Flea Market (Kolaportið) - A bustling indoor market where you can find everything from vintage clothing and antiques to local delicacies and handmade crafts.

Local Shops:

1. Laugavegur Street - Reykjavik's main shopping street, lined with boutique shops, art galleries, and trendy stores. Don't miss the iconic Icelandic design stores along this street.

2. Skólavörðustígur Street - Known for its unique boutiques and local fashion designers, this street offers a more bohemian shopping experience.

3. Hverfisgata Street - Discover a mix of local designer shops, stylish home goods stores, and contemporary art galleries in this trendy neighborhood.

Other Recommendations:

1. 1.1 Soon - A quirky vintage-inspired boutique offering a curated collection of second-hand clothing, accessories, and household items.

2. Geysir - A renowned Icelandic brand known for its high-quality wool products, including cozy sweaters, blankets, and accessories. They have several stores in Reykjavik.

3. Handknitting Association of Iceland - Visit this store to find authentic Icelandic wool products, including traditional hand-knit sweaters, mittens, and hats, produced by local artisans.

4. Gallerí Fold - A must-visit for art enthusiasts, offering a wide selection of contemporary Icelandic art, including paintings, sculptures, ceramics, and jewelry.

Please note that operating hours and availability may vary, so it is advisable to check in advance. Enjoy your shopping experience in Reykjavik!