Rick has his top sightseeing suggestions posted right on this web site:
Stockholm sightseeing << Click on At a Glance
I see he doesn't have an entry for Gamla Stan, the medieval section of town--though that's where the recommended Royal Armoury is located. I'd think a couple of hours walking around that area would be nice. Some of the streets are intensely touristy (it will be immediately obvious if a cruise ship is in port), but it's like Venice: Turn down a side street and it's peaceful.
For a good, quick, inexpensive lunch on Gamla Stan (open 7 AM to 2 PM on Monday-Friday only), I can recommend City Sallad at Skeppsbon 6. Google is flagging it as "temporarily closed", but I don't know what that's about. It was up and running in mid-June, and I don't see anything informative on the web site. City Sallad serves 2orkers in the area, some of whime stop in on the way to work to,pick up a salad for lunch. There are 9 options with a variety of proteins. There should be something for everyone. If there's no one at the counter, you just grab what you want and check yourself out on the terminal. All the salads are the same price and come with a beverage and a roll. I don't remember whether Enblish translations are posted at the little shop, but the online menu has them:
City Sallad menu
I think most general-interest tourists would appreciate the Vasa Museum and Skansen, which are probably the best-in-class of their type. The Vasa Museum can be crowded. I think Rick suggests looking at the line and making a decision about whether to return later. You could tentatively plan Vasa first, early in the morning, but detour to Skansen first if Vasa looks too busy. The Vasa Museum offers free tours in English. That will be worthwhile if the timing works for you. Ask at the information desk when you arrive.
The National Museum is a good museum of art and decorative art, if your family is interested in such things. I love Millesgarden, but it's outside the center and rather time-consuming to reach, so I wouldn't recommend it on a two-day visit unless you are true sculpture junkies.
Stockholm is a very beautiful city with lots of lovely architecture in a very nice, water-and-islans setting. Just walking from place to place is a treat. Individual city transit tickets are rather expensive, so it's worth trying to plot an efficient sightseeing route. There may be discounts for the kids, though. I don't know whether there's a well-priced daily ticket that would be worthwhile.
Where are you staying?