You should come to Little Paris in Frogner, the area from Solli Plass and up towards Uranienborg Church. Nice quiet shopping, both Norwegian designers and memorable cooks/patiseries and international designer labels. The best coffee shops, the best fish restaurant in town and a good arthaus for movies with a brain.
Karl Johans gate from the Central Station up towards the royal residence has lots of shops and shopping centers, and when you are done shopping turn to the harbour area and Aker brygge which also has a good deal of shops and restaurants. If you want more, continue through the royal gardens and walk up Hegdehaugsveien and Bogstadveien towards Majorstuen.