Go visit the Vasa. http://en.wikipedia.org/wiki/Vasa_%28ship%29

You could rent an apartment. It is probably cheaper than a hotel and you can make your own meals, at least some of them. Check out Airbnb for possibilities. Check out this link for sightseeing: http://www.venere.com/blog/stockholm-with-kids-10749/.

mybennett, I am the voice of experience... we took our (then) 7yo (boy), 9yo (girl), and 11yo (girl) there and loved it! We were there in April 2011, so the weather was a bit chilly, but we had a great 5 days!

We rented an apartment - which was awesome. We were right in Gamla Stan - which we loved! It gave us the flexibility to have extra space with kids and mainly, to eat meals in! We found we ate breakfast in (Mr. Surf would go for a run every morning and pick up fresh croissants and bread), ate lunch out as we were touring, and eat dinners in. We found a grocery store on Gamla Stan so we just stocked up there.

http://www.thecollectorshotels.se/en/victory/about-the-hotel/apartments/10-the-admiral-s-penthouse/

Things to do?
Our favorites:

- Vasa. Don't miss. Tour was about 45 minutes long and perfect for the kids. We spent a few hours total there and could have been there longer.

- Royal Palace - especially like the Horse Parade/Changing of the Guards. Different days are different changing of the guards, we saw it twice, the ones with the guards on horse was very cool.

- We did lots of wandering - when we came home from the Vasa, we took the ferry to the next island (Skeppsholmen), and walked home from there. Very fun.

- cruise around the city. We took one that was a few hours long and it was the right amount of time.

- We did not get to Grona Lund as it wasn't yet opened.

- Skansen. Had fun wandering around and watching some of the open air exhibits.

- We did spent one night at the Jumbostay near the airport. Since we had an early flight out on our departure day, we just spent the night here before. We booked the cockpit suite, which the kids thought was awesome.
http://www.jumbostay.com/

- We went for a drink at the Icebar to celebrate a birthday. Expensive? Yes... but totally fun.
http://www.nordicseahotel.se/en/The-hotel/Food-and-drink/Absolut-Icebar-Stockholm/
(again, we spent money on things like this and saved money on dinners).

- City Hall. Had a neat tour here - loved it. Then we climbed to the top also.

A few tips with kids:
- I ask mine to make a presentation before we go (usually Powerpoint). We talk about what they will see and they pick something (usually one thing) they are interested in. They teach the family all about that one thing. Then, when we get there, it makes it really interesting and the kid is extremely interested and invested. My 7yo did the Vasa - which made it so much fun to actually see it! (btw, I also make one of things I think they would like).

- After a tour, we sit down and take a 'quiz' of about 10 questions. I don't make it hard, but things that we heard or saw. For example, 'How many crowns are on top of City Hall?' (three) or "who were the Swedish at war with when they ordered the Vasa?" (Poland... which is an ongoing joke in our family, because one of the kids said, "Polynesia"... huh???) If they 'pass', they earn a lollipop ... or a mint... or a mini bag of Skittles. Which honestly, they probably would have gotten anyway, but I make them feel like they've 'earned' it.

- Loved Gamla Stan and so much fun to wander around. We went out for ice cream every night - there were two ice cream stores that we found on the island and we debated over which one was better. So we just had to keep going back for more testing! (btw, get sprinkles... the texture is different than American ones and they also have a variety of flavors. yum!)

feel free to email me - my email is on my profile. have a great trip!

Stockholm with kids is really fun! I agree with visiting the Vasa, Skansen, Royal Palace and changing of the guards, GamlaStan and Gröna Lund amusement park. My kids enjoy, and I was really impressed by, the Naturhistoriska museum (including it's Imax theater where you find some films are in English). Take a ferry ride to another island. Boat tours in the archepelago are fun.

You can stay on a ship-AfChapman hostel for an experience. We have never done that but it does get sold out early. We are in the habit of staying at the Zinkensdamm hostel/hotel on Söder. We've booked the hostel portion and the hotel portion and found the hostel room is identical to the hotel but you make your own beds and empty your own trash. Includes private bathroom/wc and cable tv etc... Can't remember about the towels...Anyway, it is a decent place and within walking distance to the tunnelbana metro and about a 10 minute ride into the center. Breakfast room gets a little crowded in the summer. It is located right by the Zinkensdamm sport field. You could check out the schedule to see what's on in the summer.

In regards to allergies-our family has none but I would bet Sweden is more accommodating to food allergies than many other places. Most places offer lactose free and soy milk as substitutes for example.

Places to eat- try something from the hotdog stands. There are several located by Gröna Lund if you are there. Not sure if they sell "tunnbrödsrullar" in Stockholm but that would be a soft flat bread with mashed potatoes, hotdog and a little relish, ketchup and mustard if you like. Don't forget to ask for bread with your hotdog (korv). And don't be surprised if the little fork/knife combo breaks while you are trying to work your way through the thing. (they usually do). Best bargains are at lunch time when you can order a meal for a fraction of the evening prices. Don't miss out on coffee and cinnamon roll (kanel or kardemumma bulle).

Enjoy your travels,
cheapboxofwine

Here are some good things to do with children in Stockholm:
The Vasa museum. It's fantastic to see a real big warship from 1628! (www.vasamuseet.se)
The changing of the guard at the Royal Palace.
The Gröna Lund amusement park. (www.gronalund.com)
The Skansen park with animals and many other things. (www.skansen.se)
The Junibacken is about the stories from Astrid Lindgren. (www.junibacken.se)
The Kaknäs tower gives a great view of Stockholm. (www.kaknastornet.se)
If you have time, you should also make a trip to the Stockholm archipelago with about 24000 islands just outside Stockholm.

Yes, July is in the swedish soccer season.
The exact schedules are not ready now however, with a few exceptions below.
At 20 July there will probably be the first soccer game at the new stadium "Tele2 arena" with 30000 seats. (www.tele2arena.se)
At 28 July there will be the European Chamionship final game for ladies at the new "Friends arena" in Solna just outside Stockholm with 50000 seats (friendsarena.se) (www.uefa.com/womenseuro/finals/). The first soccer game in this new stadium was only 11 days ago.
There will be other soccer games also with the three big soccer clubs in the Stockholm area (AIK, Djurgården and Hammarby) but the schedules will be decided later.

We haven't traveled with kids since they were young..now at 58,56 and 51 they have their own families. I concentrate on our 6 grandchildren, offerng them a month or a little more in Euroe when they graduate college..thus far three of them, three to go.

We love Stockholm and have traveled Sweden from Narvik in Norway though Kiruna and Uppsalla. The suggestions you have above really cover children's activities very well.

Additionally, Drottningholm Palace would be a 30 minute pretty boat trip, with beautiful grounds. It leaves from the little pier behind the unique city hall..the kids would like climbing its tower. Also, I think the kids and each of you would like to see the very colorful changing of the guard

You may want to try The Clarion(?) Mornington Hotel, easy walk to Gamle Stan and the harbor. For Stockholm, "reasonable".. It's also a block away from one of the cities many Food Halls (Sala).

Here are some selected pix for you..
Stu

https://picasaweb.google.com/stuarttower/Stockholm#

You may want to stay at Scandic's Hotel Hasselbacken which is on the same island as Vasa Museum and next to Skansen. Djurgarden, the island's name, was the formerly the royal hunting grounds so there is parkland for kids to run around. Good bus and ferry connections in front of the hotel.
The little ferry takes you over to Gamla Stan.