Currency exchange will be a pain. Neither Norway, Sweden, nor Denmark are members of the Eurozone, so you'll be using the Norwegian krone in Oslo, the Swedish krona in Gothenburg, and the Danish krone in Copenhagen.
I've been to Copenhagen several times on business, and the city is very friendly, approachable, and walkable. Everyone speaks excellent English, but it's always a good idea to learn a few basic phrases in the local language, especially "thank you."
If you have time for sightseeing, you'll want to check out Amalienborg Palace, the Marble Church, Nyhavn, Rosenborg Castle, and the pedistrian shopping area near Nyhavn called Strøget.
As for food, there's a ton of restaurants around Nyhavn and Stroget, but I haven't really found anything that was outstanding--most of the restaraunts are very pricey and fairly touristy.
I haven't been to Oslo or Gothenburg, but if the prices are anything like Copenhagen, bring lots of $$$.
Have a great trip!