Copenhagen has something for everybody!
Pretty much everything below is located centrally, which means you can either leg it, use the tourist bikes or spring for a daypass and use the Metro.
Must see:
You've mentioned that you're both metalheads, so I'm not sure how interested you are in spending some of your limited time taking in the culture and arts etc., but here's a mix if you're feeling touristy.
- The Little Mermaid statue located by Langelinje Kaj, one of our biggest attractions (you might laugh at that when you see it)
- Christiania (an alternative place located in the heart of Copenhagen, originally carved out by hippies as a free haven)
- Nyhavn (cozy place for a beer and some lunch, but be warned: it's a tourist magnet and pretty expensive!)
-- PROTIP: I would suggest taking one of the seaside tours of the city with one of the boats. It'll take about an hour, but it's a nice way of viewing many of the buildings both new and old, and the guides are pretty knowledgeable.
- Tivoli Gardens (a relatively small amusement park located in central Copenhagen, has rides for all ages and can be a fun way to spend some hours while still being in walking distance of a lot of other stuff)
- The Blue Planet (Northern Europes largest aquarium, located a short trip to the outskirts of Copenhagen next to the Airport)
- Strøget and Field's, if you want to do some shopping.
As a local, I would suggest Christiania, Nyhavn and the boat tour.
Must eat:
- Torvehallerne, located next to Norreport station in central Copenhagen. Fantastic place with lots of different foods and something for everybody. Highly recommended for a quick lunch.
- If you want to sample a local favorite, the so-called "Smørrebrød", I suggest having lunch at: Øl & Brød located at Viktoriagade 6 OR Møller Snaps & Smørrebrod located at Toldbodgade 5.
- Cocks & Cows, Halifax or Sliders, that all have restaurants located centrally and I believe their webpages have en English language version, so just browse for a location which is convenient for you. Good burgers.
- MASH, Köd OR Retour Steak, same as above for locations. Great steaks.
I eat out often, so I can recommend a lot of places, but it's easier for me if you mention what kind of pricerange and kitchen(s) you're after.
Must drink:
Gonna assume you're Beer folks!
- Mikkeller Bar, located in Viktoriagade 8. Fantastic beers, but may seem a little pricey.
- Ørsted Ølbar, located in Nørre Farimagsgade 13. Good range of beers, enjoyable establishment and affordable for everybody.
- Warpigs, located in Flæsketorvet 25. A joint venture between the Danish "Mikkeller" and the American "3 Floyd's". You can get some great beers here, and you can even eat some BBQ here too if that's your thing.
- Kølsters Tolv Haner, located in Rantzausgade 56. For the beer enthusiast.
If I assumed wrong and you're looking for something else, just let me know what your preferences are and I can narrow it down for you.
Hope you have a great time in Oslo and Copenhagen; both cities are, in my opinion, fantastic
