All Walt Disney World resorts have activities for kids but the Polynesian seems to be popular with families for two reasons. One is the transportation makes it easy to spend less time getting in and out of the parks, and the second reason is because of all the activities that the Polynesian has to offer kids.
I have been to the Polynesian many times as just a couple and my last few visits were with a child. We also have traveled with families that have multiple kids from young to teenage so I have gotten feedback from what they enjoy about the Polynesian.
For those staying concierge you will find that the lounge is very kid friendly. It has a kids table with snacks and smaller chairs over near the TV that plays Disney movies during lounge hours.
I will separate all the activities into two catagories, Free and Pay. You will find that the "free" list is longer than the "pay" list.
On the next page is a list of activities at the Polynesian.