Bakery Sandholt is a small, family-owned, gourmet bakery and coffee shop in downtown Reykjavík. They offer a wide variety of artisan breads, cakes, pastries and even hand-made chocolates. They open early, so you can go there for breakfast before exploring Iceland, and during lunch they serve soup and sandwiches. 

They are located right in the middle of down town, on Laugavegur, which is the main shopping street in Reykjavík, so you can stop by here after exploring the island, or stop in for a break while out shopping with your friends. There is always something new going on, some seasonal pastry or festive confection, so stop by every time you're in town and be surprised every time.