Here is my new knitting basket. After looking at various web sites (thank you so much for all the recommendations!), I ended up going with something from Pottery Barn anyway. This is the Havana model I think. There's also the Savannah which is the same style basket in a lighter color.
I chose it for the size (actually I was even hoping for something larger) and the lid. In magazines you always see these perfectly organized knitting baskets with color-coordinated skeins of yarn all exactly the same size but my knitting collection tends to be much more chaotic so a lid is appreciated. So far Bubbles the rabbit seems uninterested in chewing it.