Going to Copenhagen tomorrow and then Stockholm

I am on a long weekend trip with my other half. I will reach Copenhagen this friday and then go to Stockholm on sunday until monday evening.
Any advice on what to do, where to go, what to eat and nice kitchen shops while we're at it?
Also it would be great to meet up if you have the time!

Vasa museum was quite impressive
http://www.vasamuseet.se/en/

Thanks, will go there, it looks really good!

You're into beer, right? Check out Akkurat at Hornsgatan 18. Not sure what kind of dining you like but you could pass by Östgötakällaren at Östgötagatan 41 and have a look.

I really enjoyed Torvehallerne in Copenhagen. I ate at Kalaset cafe every morning. It was super good. I highly recommend the chocolate banana pancakes and the hot chocolate... And their breakfast. I tried eating breakfast in other places that I saw had good reviews online, but I ended up at Kalaset right after. I pretty much ate 3 meals at breakfast and waddled it off.

For Stockholm +1 to the Vasa museum!

Thanks for all the recommendations!

@Mari, I was at Torvehallerne this morning and did check out Kalaset, it was good

@jigert: looking for a relaxed place where the locals go, so your recommendations fit the bill, very interested by Akkurat