Værnedamsvej has a great number of different stores, and if you consider yourself a bit of a gourmand, you should definitely stop by here to snoop through the stores. There's everything from one of the city's well-reputed butchers to groceries, cheese, cakes and a great wine store.
If you're a foodie, this is a great stop. On a summer day, get yourself some wine, some cheese and make yourself a little lunch to bring to the nearby lakes. Al fresco eating in the middle of Copenhagen on a summers day is great for people-watching.
The shops keep regular opening hours, so get in before 16:00 to see it all. Otherwise, there's some decent eateries on the street.