Fantastic wonderful country. We have family friends there and I have been going for hols on and off since I was four. Went last summer (after a long time away)for the first holiday on my own with the kids and we had a wonderful time both when we visited friends and when we went off on our own. Really child friendly - as I remembered from being there as a child myself.
Took the kids to Stockholm for a few days as they had never been there and frankly - alcohol aside - it wasnt't THAT expensive for a capital city. (Get a 'Stockholm card' - we got them as part of the hotel package and got loads of things like tubes, buses, trams, boats, museum entrances free - I think they must have owed us by the end!)
Then we headed off on our travels - public transport all the way - easy peasy. Ended up on Gotland in the Baltic and cycled and cycled... really very easy even for a bit of a light weight like myself as it is so flat! If you can manage the extra travelling it is a magical place but other bits of Sweden are great too - I am most familiar with the north but have also spent time in Malmo and that has it's own attractions.
When we weren't staying with friends we stayed in youth hostels which were fab - and quite easy on the pocket. We are planning to camp next time.
And did I mention that the sun shone and shone and shone!? Now I know that can't be guaranteed but it was lovely. We swam in the sea practically every day on Gotland. Sweden is especially good for those who like the outdoors!
The three of us couldn't have gone anywhere better to forget about what was frankly a god awful year - my daughter especially can't wait to go back.
So - yes it is a bit more expensive than some other European destinations but if you can cut back on the booze and get creative with self catering etc it's not so bad (and I like a glass of vino as much as the next person but, gawd, was I healthy when we got back!)
Enjoy!