Rather than wax on about what to do in Stockholm, I'm just going through my pictures, and my notebooks, and give you the list of what we loved the most (and not everything in this one post--I have save something for the rest of the week)...
The Royal Palace: watch the changing of the guards, and then the kids can play dress-up in the Royal Armoury.
The Vasa Museum: a ship that sunk right in the harbor, and was dug up and still so well preserved, that they turned it into a museum. Awesome.
These are my cards from the places I really loved...of course they are probably way too small and annoying to try and read, so I'll give you the greatest hits:
If you need to rent a stroller: Bonti rents them by the day. We picked one up at the store, and then they picked it up from our hotel.
Best Food Court Ever: Ostermalms Saluhall. It's an indoor market with some great restaurants, the best being Lisa Elmquist, a fantastic seafood restaurant. You must order the skagen--which is something like a shrimp salad on white bread.
Tuss: really classic, simple lines, kid clothing line.
Asplund: nice shop with the best in Scando design.
Skeppsbron32: kids shop that had the coolest modernist doll house, made by Lundby.
Ecovarhuset: where to pick up organic diapers, organic shampoos, creams, etc...they also have a whole line of chic organic clothes.
Androuet: great cheese store.
Ohlssons: fabric store that had waxed linen in white, black, and natural, for cheap--and we bought it for our outdoor tablecloth.