The main shopping street in the centre of Reykjavík is Laugavegur. It will provide you with many small and exciting specialty shops, competitive fashionwear and designer labels.
For art lovers, the Skólavörðustígur is a must - a street wich runs from the Hallgrimskirkja down to the Laugavegur. There you will discover a goldmine of arts and crafts galleries and even jewlery design studios.
For those who prefer to shop indoors, there are two big shopping malls, Kringlan and Smáralind which belongs to the neighbouring Kópavogur.
If you are a bargain hunter, you must visit Kolaportið, a big indoor market which is held every weekend between 11:00 - 5:00 in the center of Reykjavík.
Take a look at this interesting website about Reykjavík as it is today: http://www.visitReykjavík.is/