I haven't ridden the Katy, but I have been to the wine country surrounding it, as my BIL lives outside of STL.
Just from what I saw, I would agree with Indy. I think parts of the trail would be interesting, but I've done riding in similar settings/geography, and although the idea of flat and off road is good, especially for kids, it would bore me to death. And Melavai has a good point. I am spoiled by my beautiful surroundings at home. But, like anything else, I get immune to it. I've been riding in places where people have raved about the scenery, and I'm like, "huh, what?" The Finger Lakes is one example. To me, I need something scenic enough to really stun me, or the area has to have other redeeming qualities, such as culture, history, or food. When I travel, I want different.
I applaud you, Limewave, for doing a family trip. I wish I had done this when my kids were little. Idaho sounds great.