Moderna is situated on my favorite island and is neighbors with the also very nice Museum of Architecture. Moderna is the most visited art museum in Sweden. It’s big, light and has one of the most creative and fun art shops in town. Their collection of artwork is really nice and their temporary exhibitions are usually excellent, they have a couple of large ones every season. Right now there’s a bunch of interesting exhibitions, go see!
Moderna has something for everyone. All exhibitions have guided tours, which are included in the admission, check their website! For the art in the museum’s collection you can borrow audio-guides for free.
If you’re younger than 30 and are planning on staying in Stockholm for a while, I recommend you to buy the “Friends of Moderna Museet” card for 250kr/year. You get invited to previews, get 20% discount in the art shop and free admission to several other museums like the Museum of Architecture and Nationalmuseum.