Do not miss Fritjof Nansen's ship the 'FRAM' and the other boats exhibitions in Oslo - (unless of course you happen to hate boats, then I suggest you do something entirely different!) .
Nansen was the father of polar exploration but unfortunately not many people seem to know much about him outside of Norway... Then there's Thor Heyerdahl's Hon-Tiki museum - with it's giant replicas of the Easter Island statues... And of course the Vikingskipshuest (excuse my spelling if wrong) which houses some of the most remarkable (again only if you like boats) collections of Viking long boats.
Lets assume you don't like boats... well then there's the Norwegian Folk museum which just happens to be near to all those boats. It's got all sorts of things to do with.. well... Norwegian Folk thingys.
If boats and folk museums don't (excuse the expression) sail your boat, then you can visit the Vigeland Park. He was a sculptor, a pretty busy one too by the amount of his work on display in the outdoors of the park.
Enough sculpture? Well for me being Irish when we get a centimetre of snow the country closes down. Completely! Despite this I've always been fascinated by Ski Jumpers. That peculiar grouping of people who feel the urge to hurtle down 1:1 gradients covered in snow, wearing skis.... oh yes and there happens to be a bloody big drop at the end.
What I'm trying to say is 'go to Holmenkollen' where the ski jump is housed. Even if there's no snow it's well worth a visit.
I hope that's enough to get you started. If I get time I'll try fill you in a little on Stockholm.
P.S. Whatever you do, DO NOT, repeat DO NOT!!! order an Irish Whiskey in any of the bars, unless of course you want to pay 30euros for the pleasure. Believe me.