If you're downtown, you might as well pop by København K and check out their selection in vintage threads. If nothing else, you will be able to get an outfit that blends you in with the crowd at nearby shopping street Strøget.
Seriously, though, this place has a nice selection and reasonable prices, especially compared to some of the price gouging going on in some of the other second hand shops in the area. Well worth a visit for a quick look around.
Mon-Th: 11:00-18:00
Fr: 11:00-19:00
Sa: 11:00-15:00