Before you book - as the flights are routed via main airports in Germany (Berlin or Dusseldorf) this also gives great solution to end your trip there and do not continue to the final destination. You may also reverse your routing i.e. fly from Copenhagen and return back to Stockholm (via Germany). Some of the flights are offering long layover in Germany.
If interested please look for travel dates within January and March 2015. Please refer to below booking samples to New York and Chicago. If you would need to book your hotel you may compare via our tool - hotels in New York or Chicago.
Booking samples
DE . Stockholm - New York - Copenhagen (via Germany) for €225
EN . Stockholm - New York - Copenhagen (via Germany) for Ł188
DE . Stockholm - New York - Copenhagen (via Germany) for €219
DE . Stockholm - New York - Copenhagen (via Germany) for Ł183
..or you may also consider to book directly with Air Berlin
All cities, Stockholm, Copenhagen, Warsaw or Budapest, are easily reachable from other European cities by many low-cost airlines. We recommend to use service of Skyscanner to quickly find out which low-cost airline is connected from your hometown.
Booking sample of cheap flights to New York or Chicago from Europe for €219 here. In this case you would be departing from Stockholm to Chicago on 10th of February and returning from USA back to Copenhagen on 24th of February 2015.