We were in Amsterdam for five days in 2007, and here were our favorite things we did when we were there. Since it was just Clara and myself, we spent way less time exploring, because it was just harder not having Matt there to help (she was still in a stroller then), and it was cold. So, this is by no means a guide to Amsterdam--it just happens to be what we did, and liked.
3. Vondelpark (6 play areas)
4. Laura Dolls (vintage kids dress-up that is way cool and not expensive--we got Borsalino hats there for 5 euros, and they're still in the dress-up box)
5. Keet in Huis (maybe the coolest ever kids design shop, in a cool area--walk around there and explore the 3-4 stores all next to each other. Sissy Boy is one of them, and they have great little restaurant, and a nice edit of housewares.
6. Renting a bike and tooling around (just watch out for the tram tracks--we almost bit it with the bike tire getting caught in one)
7. Buying a Miffy in the land of Miffy
8. The Nine Streets area
10. Hema, the Target of Amsterdam, had super cool+basic kids clothes.
11. Noordermarkt: a Saturday organic farmers market (there's a bathroom in the church right next to the market)
(Keet in Huis store)
(Inside the Lloyd Hotel)
(Laura Dolls, above and below)
A couple of good sites to check out before you go: Babyccino Kids Amsterdam, 21st Century Amsterdam, and also try this book I just posted about.