If you plan to be in Copenhagen, I suggest planning a few days in Sweden. The best way to go about it to plan for a day trip to either Helsingborg (travel via ferry) or Malmo (travel via train). Both are worth visiting on day trips, though there's much more to see in Malmo than in Helsingborg. Malmo is also closer to Copenhagen.
Copenhagen to Malmo by train only takes 35 minutes across the Oresund Bridge. I prefer this option because if you're driving you will have to pay bridge toll. If you're on a budget, the bus is the better option as it only costs $15 (DKR 100).
I would strongly suggest you not to skip following places once you visit Sweden - 1. The Göta Canal 2. Kiruna, Lapland 3. Abisko National Park, Lapland 4. Liseberg Theme Park, Gothenburg 5. Oresund Bridge, Malmo I have Sweden Road Maps, Tourist Guides, Travel Videos of Sweden and everything which can make your journey great!
I am planing trip from Copenhagen to whole Scandinavia like Sweden, Finland, I will write here some of my adventures from that tour!