As for Stockholm, I don't know how much time you have, but Akkurat is a must. Their cellar (full of vintage/whale lambics and a lot of other stuff besides) is out of this world and one of the reasons this is one of the world's top beer bars. Also, you can always get at least one fresh Cantillon on tap.
As for other things, I would recommend the Vasa Museum (
http://www.vasamuseet.se) even though it is kinda touristy. It's a more-or-less perfectly-preserved 17th century battleship that they've build a museum around, and you can walk around parts of the battleship, see the insides etc. And 17th century battleships are cool!
Gamla Stan (Old Town) is also touristy but I like it because I'm a history buff, most of the buildings are original 17th century, there are cool narrow alleyways, cobblestones, the Royal Castle etc etc and if you like whiskey you can hit Ardbeg Embassy on Västerlånggatan.
If you need a more detailed list of beer places, just holler and I'll get some links together.