I think the best is walk around the city center and take some boat-trips to see the Archipieago, the lake and the locks...
If you visit the Tourist office you can have a brochure about this boat-trips and buy the tickets the same day...in the pier.
Agreed. Wander around Sodermalm. Hang out in one of the hundreds of bars. Be prepared to spend all your money
I'm just back from Stockholm and I'm totallu agree with the others
A stroll in the Gamla Stan early in the morning or late in the evening is something not to be missed, and a boat trip to the archipelago is also a must. Regarding museums - the Vaasa museum was breathtaking for me.
And for accommodation try a hostel in the harbour