We took our (then) 3-year-old to Salzburg and the Salzkammergut region a few years ago, and it was the best vacation we've had. We stayed in a farmhouse on the Moosstrasse in Salzburg, can't remember the name of it, but it's in Rick's book. It was an easy bus ride into town.
For kid stuff in Salzburg, make sure you do the fortress, our son loved it. There's also a nice playground right next to the gardens at Mirabelle. Definitely don't miss Hellbrun -- the fountain tour is a lot of fun, and they have a great playground there, too.
From Salzburg, we stayed for a week in St. Wolfgang, which is about an hour outside of Salzburg. The region is full of little towns sitting on lakes. If the weather's nice, there's some "beaches" by the lakes where you can swim. There was also a petting zoo in the area with deer, mountain goats, and elk. Plus there's tons of hiking in the area.
We stayed at a farmhouse there. I'd definitely recommend a farmhouse stay if you're renting a car. The farmhouse had cows, ponies, chickens, and ducks. There were 4 other families staying there, so there were lots of other kids to play with. It was great -- after dinner, we'd sit with the adults and drink beer and play cards while our son played with all the German and Austrian kids there. Many farmhouses rent out apartments, so you can eat in if you want.
I didn't think there was much for kids to do in Hallstatt, outside of the ice caves (ours was too little for the salt mines). They have a playground there, but it was right on the lake with no fence around it.