There's so much to do both around Stockholm and out in the Archipelago that it's impossible to fit it in on this page. Instead here's my top 5, and further down you will find links to official guides in English that will give you 1000's of tips.
1. The Archipelago
With it's 24,000 islands a trip further out in the archipelago is a must. Either
you sail yourself or, a much easier way, you jump on one of the many ferries
(there's even a boat taxi you can call). Within half an hour you can be having
a superb lunch or dinner on islands like Sandhamn, Fjäderholmarna or Utö. Stavsnäs
By close to the house have auctions every weekend and a lovely village bakery.
See more information here: Stockholm
guide / Archipelago
2. Stockholm
Beauty on water. Stockholm is built on a number of islands surrounded by water
(but a lot cleaner than Venice :-) Just walking around the Old Town and
looking at the sights is enough, but don't miss out on it's superb restaurants,
museums/palaces, the "Skansen" Zoo and park, the
"Gröna
Lund" amusement park, the "Wasa ship" museum etc. See it by foot,
on canal cruises or from a hot air baloon. Shopping is also good and with the
Krona being very low, everything is quite cheap.
More information here:
General guide: http://www.stockholmtown.com/
General guide: http://cityguide.se/stockholm/
3. Birka vikingtown
Founded 760AD much of the town is yet to be excavated and archaeologists
return each summer to discover new facts about this fascinating place. Boat
from Stadshuskajen in Stockholm.
More info: Birka
4. Drottningholm
The beautiful Royal Palace situated just outside Stockholm by the lake
Mälaren.
More info: http://www.stockholmtown.com/
5. Mariefred (Gripsholm castle)
Take a steamboat cruise out to this picturesque town with it's old Gripsholm
castle with beautiful views over lake Mälaren. Boat from Stadshuskajen in
Stockholm.
More info: http://www.stockholmtown.com/
MORE LINKS
Stockholm guides
http://www.stockholmtown.com/
http://cityguide.se/stockholm/
http://www.nojesguiden.se/
http://www.aftonbladet.se/stockholm/stockholm.html