I'd like to recommend the Tomamu Resort in central Hokkaido. But if you prefer to go where all the Aussies go, then it's the Niseko Resort, also in Hokkaido.
I say Tomamu because it will certainly keep your kids occupied. Besides the excellent podwer snow, it has by far the largest indoor swimming pool with waves that I've seen anywhere in Japan. (And Japan has huge indoor pools.)
It has at least two arcades (for games) as I remember as well as many shops and restaurants.
The only drawback as far as cultural interaction is that the Tomamu Resort is secluded from the rest of the area. It's like a little town of its own. But that gives you complete security, too.
You can cover this shortcoming by staying in another part of Hokkaido or anywhere in Japan for a few days after the skiing. In Hokkaido, I recommend Otaru, which is only an hour from Sapporo. The Noboribestu Onsen is also excellent though it may be too far from the Tomamu.
http://www.snowtomamu.jp/
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