Kevin,
There is a member here with the screen name vanpoodle. Although I haven't seen her on recently, she is probably the most knowledgeable about London.
One of her posts (#9) is in this thread:
London Hotel Zone Information
You might find her discussion about zones interesting.
To your list, she adds quite a few. If you can find a hotel in the more central zones you might not want to go to the more outer ones on the list, but you can at least take a look at them. You can zoom in on the Priceline zone maps. When you get in further, you can see the little symbol that indicates a tube station. A red circle with a blue bar across it. You can get an idea just how far you might have to walk to reach one of the stations. The stations tend to be closer together in the more central zones.
If you click on her name you can also read some of her other posts.
Although a couple of times I've landed the Copthorne she mentions as some place to avoid, and have been happy with it. You can read the reviews both here and on www.tripadvisor.com and decide for yourself if the things to which people object would be problematic for you.
Also, on Priceline some of the zones have more information about the attractions in them. If it is available, it is listed under the zone map when you click on "detail map" of a particular zone.
And while I'm at it, if you don't have some already, it would be well worth your time to pick up some London travel guides at your local library or bookstore. Lots of good ones, but my personal buy-and-carry-with-me favorite is Lonely Planet. Great maps and directions, yet concise and lightweight.
But to actually answer your question about the zones you've listed - yes, I think all of them would be suitable for your family. And you might consider some more after you've done some more research.
Romelle