If you want to go shopping you have the option of visiting variety of small shops on Laugavegur which is the main shopping street in Reykjavik and is in the heart of the Reykjavik City center.  Crossing Laugavegur and leading up the the 'big church' Hallgrimskirkja is a street called Skólavörðustígur. On Skólavörðustígur you´ll find many small gift shops and art galleries and is an excellent place to look for something interesting. Many cafes and restaurant are in the area so take your time to sit down and enjoy the scenery.