Google should produce a number of results for Yellowstone River trip reports. Do you know which part(s) you would be interested in? I believe you can avoid most of the whitewater by putting in east of the Park. I've looked into a trip from Pompey's Pillar - just east of Billings - to points east. The Laurel - Billings areas have refineries right on the river, and I would guess it would be desirable to skip those stretches. Otherwise it's wide open country.

I have paddled the Upper Missouri further north. That is more of a remote wilderness setting. The Yellowstone has I-90 running most of its length, but the Missouri has just a few road crossings.

Ranger