When I have been traveling with kids, I have found that it works best when I plan highly active activities to alternate with ones that allow time to rest and recuperate. This philosophy has worked for me personally, and influences my recommendations below. Furthermore, all of the attractions and activities listed below are available on the Stockholm Pass (sponsor), which can save you a lot of money compared to paying for individual tickets and admissions.
So, without further ado, here are my Top 7 Kid-Friendly Things to do in Stockholm.
1. Skansen- Open Air Museum
theater. You can top on the Story Train to experience some of the tales of Astrid Lindgren, or experience my personal favorite: Pippi Longstocking's house. As a little girl, I was completely fascinated by the tales of Pippi Longstocking. I loved the films, the books, and would walk around singing the theme song. Even as an adult, the Pippi Longstocking house is an incredible life-like experience. Junibaken has a cafe where you can easily stop for a bite to eat. It's location is near a lot of attractions including the Vasa Museum, and could easily be paired with a number of other thing's you'd like to see. It is easily accessible by the Hop On Hop Off bus and boat, as well as, by public transportation (the tram).
4. Grona Lund Tivoli
5. Under the Bridges of Stockholm (Boat Tour)
you'd be happy with any of them, I would highly recommend this one in particular. We went to the ticket counter early in the morning, and more or less had our choice of time slots. We chose a tour at 1:00 in the afternoon, which is perfect for a two hour boat ride. By 1:00, we had already been on our feet a good long while, and were ready for a bit of a break without losing valuable sight seeing time. This particular tour is on a relatively small boat, single level, with booth-like tables that seat roughly six. There is a snack bar available as well. The snacks available aren't anything you couldn't just as easily have purchased at the grocery store (sandwiches, beverages, etc), but significantly more expensive, so I recommend popping into a store and buying some items for lunch to bring aboard. I noticed many people doing this, and on this particular tour, the staff didn't seem to mind. Plus, it will save you a lot of money. This tour is pretty straight forward, just like the Hop On Hop Off buses and boats, there is a headset to narrate your tour. Plus, you see some of the most beautiful parts of Stockholm, areas that might otherwise be difficult to access. Again, this is really easy to access via public transit or the hop on hop off bus or boat.