When you purchase a ticket for the Museum of Medieval Stockholm, you gain free entrance into the Stadsmuseum as part of the package… for an entire year. And, while the Medieval museum is geared mostly towards kids, the Stadsmuseum is not.
The Stadsmuseum is off the well-beaten-tourist-path, as is the nearby Fotografiska. Because of this, I think that the museum doesn’t get as much traffic from tourists (or at least it didn’t seem to like other museums I visited). But the Fotografiska and Stadsmuseum are close enough to each other, that if you take a cab to Fotografiska, you can stop by Stadsmuseum on the way back to Old Town. Both are worth it.
The Stadsmuseum is housed in a 17th-century palace and doesn’t focus on one particular era of Stockholm; it’s a rather eclectic mix of art, history, entertainment, and popular culture. This is not a bad thing. It’s very easy to get lost amongst the various collections. The big draw for people is the city walking tours with the most popular being a Saturday morning walk that recreates the path taken by Stieg Larsson and Lisbeth Salander (Girl with the Dragon Tattoo).
Also offered is an Abba Tour of the city, which should be coupled with a visit to the newly opened Abba Museum (which is really far out of the way; the best way to visit is on one of the hop off/hop on tours).