Sweden was the first Scandinavian country I visited, and my least favourite, but that's not to say it's not a nice country. It's hard to compete with Norway and Denmark.
One thing I do remember is that when I left the airport and took a breath in, the air quality felt amazing here.
What to See
The old town of Stockholm is very large compared to other European old towns. Along with the usual touristy shops, bars and cafes, there are many museums, churches and of course the Royal Palace. One of the most popular places in Gamla Stan is Stortorget, the oldest square in Stockholm. The tall narrow colourful houses are quite a common postcard picture from the city.
I'm not really into ships, however I found this museum about an infamous ship to be truly fascinating. This huge museum houses the Vasa, a ship that sank in Stockholm 1628 during her maiden voyage. It's amazing how good condition the ship is in. The ship sits in the centre of the museum as you walk around, up and down various displays telling the story of the Vasa. Even if you're not into ships, there's a good chance you will find this a truly interesting story and I think you'll be in awe of the size and condition of this 300 odd year old ship.
Abba Museum This isn't something I visited as I'm not much of an Abba fan. However I am sure there are many out there who would love this museum. The museum goes through the history of the band and there are numerous interactive exhibits too. I understand that there is even a karaoke section to the museum, where you can sing your heart out to popular Abba hits.
Katarinahissen is a great spot to see the city from above. There's also a fancy restaurant here if you want a view whilst you eat. Or you can just take the elevator or the stairs to the top, then walk along the platform to get some great photos of the city. It's especially stunning here during sunrise and sunset.
The Royal Palace
I'm not really one for palaces unless they have something special about them, so I didn't pay the fee to see inside. But from outside this building appears to be enormous. It's within the old city, and stands out from the rest of the buildings in the area. I think that anyone who is into palaces will be fully content with exploring the interior of this grand building.
If you're in Sweden, you should probably try Swedish meatballs. I visited a cafe called "Meatballs for the People" and they were delicious! Unlike Italian meatballs, they are served with a type of mashed potato and sauce/gravy. They are made from various different meats, including reindeer, you can usually choose which meat you'd prefer.
Junibacken A museum for children which I didn't visit as I'm not a child and don't have any children. Although that's not to say that I may not check it out if I visit Stockholm again. It's a museum focussed around the Swedish author Astrid Lindgren. The name may not ring a bell, but it's likely you'll know her famous characters such as Pippi Longstocking or Karlsson on the Roof. There's apparently a train journey where you're told a short Astrid Lindgren story, and a cafe which sells meatballs. Sounds good to me!