What is the best website design for kids?

It will depend on what type of niche in that market you're aiming at.
Toys and clothing will have different look and feel.

What you could do is define some keywords, google them and look at the top sites. If the niche is well populated, you'll find some very well designed sites.

Kids like everything bright and coloured. So try to make it that way, use a lot of pictures and animations. Use big coloured letters so it will attract them to read.

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