You need to have Swedish money - they don't accept Euro and any other currency at most places!

Go there when it´s warm, never on a winter coz its less lively.

Besides all other good ideas above, I have to recommend Europe's best dim sum place (in case you're into Chinese/HK food) Aroydee which is located in Old Town. Even China Town in Nyc or other major cities outside HK can't compare to this food as it's well cooked of fresh ingredients. I travel alot, and this is definitely my absolute favorite place for dim sum, which I eat often. They have decent number of dishes to select from while prices are quite moderate... not really as cheap as one would like, but you won't have to consider washing dishes for them instead of paying, either.;)

Old town, Nordiska Museet, Skansen in Stockholm. Uppsala is a nearby city worth seeing. And the world's largest Ikea is in Kungens kurva, if you are into that. I recommend Lonely Planet books if you are looking for useful info and other than the most obvious sights.

Get a Swedish pocket dictionary and buy a Stockholm map at a newsagent's, otherwise you ll be lost...The Cinderella party ship by Vikingline is great to Mariehamn

Check out the Police Museum in Stockholm as well as the Vasa museum. While expensive, consider goign to the Grand Hotle for a traditional smorgasbord meal. The island ferry curises are nice but it may be a bit cold this time of year. Head north to enjoy some Swedish countryside and if you're travelling around a lot consider buying a scanrail train pass.

If you are there long enough, take one of the regular cruises out into the Archipelago. Several ferries leave Stockholm for just this trip or on their way to Finland or Aaland/Gotland.

Many nice museums, quite good food and very good spots to go out at night... cafe opera and sturecompagniet

take time to see the museums and the old town. tons of nice little shops and restaurants. definitely worth seeing.