Across from the lakes on Østerbrogade you'll find the best shopping in Østerbro
The street I live on is a street with great shops. If you go down the 2--3 kilometres road I live on down the way to the city center there are a lot of shops that are good; cheap as well as expensive.
Lots of shopping and great dining spots. If you continue walking you'll get to the lakes of Cph and Nyhavn (the old appartments at central Cph).