For any place, this guide is a good start
As a travel enthusiast, I recommend a high or the highest point in a new city first. Following are points with good views in Stockholm in my personal order of preference (Take the details from the guide mentioned above)
I hope you would get at least 2 full days of sunlight in those 2 days if you haven’t planned the dates yet. Good (festive) days to visit are around 6th June OR Midsummer (the Saturday nearest to 24th June.)
The central part of the city which is mostly under the buildings and structures section of the guide can be done in 4 hours with a map and a good sense of direction. The most important ones in order of my preference
1. The City Hall – The hall where the Nobel prizes are presented (except the Nobel peace prize which is presented in Oslo)
2. Royal Palace, Stockholm Cathedral, German Church and a few other churches (kyrka) are in the city center and close enough.
3. Must walk through the streets of Gamla Stan, and take a break while having a cone as if there is nothing else to do in this world.
4. Kungsträdgården, one can consider it a part of the city center tour. Good time to visit it is any summer weekend evening.
5. The Stockholm Archipelago Tour (Strömma Kanalbolaget) is a must do in a 2 day visit. if you get a good sunny day with no rain/cloud forecasts.
6. Drottningholms Palace (a bit away from city center, but I think its worth a visit, you can ignore this if you have been to Chateau de Versailles in Paris)
Of the Museums 2 most important and unique to Stockholm are
1. Vasa Museum (built around a sunken and restored ship, visited by most Europeans)
2. Skansen (world’s first open-air museum and a must visit on either 6th June or Midsummer)
A Ferry trip
1. Ferries go from Stockholm to Helsinki and Turku in Finland.
i. Turku – The trip is a 24 hour return trip with just an hour in Turku, but that doesn’t matter since the purpose is to be on the ferry. If you are crazy (like me) you can get off and go to Turku Slott (a castle) near the port.
ii. Helsinki – The trip is approximately 36 hours with around 7-8 hours in Helsinki. You can see the central parts of the city at least. You can have a good plan for Helsinki using Wikitravel.