Rental car is definitely best. 99% of the fellow travelers I've met agree that the Mosel Valley (Trier to Koblenz) beats the Rhine Gorge. Thanks to Germany's high speed expressways, it is doable, but its not a good idea as most of your time will be spent traveling instead of sightseeing. The high points along the Mosel are the steep river hills & vineyards, Bernkastel, Trier (once the capitol of the Roman Empire and the oldest German city. See the giant basilica (which was the office of the Roman Emperor), Berg Eltz, and Cochem. The road from Trier to Luxemburg crosses the Mosel at Renmich where there is a fine Roman villa on the German side of the river. Just upstream from Remich is the small town of Schengen where the famous treaty was signed on a boat in the river where Germany, France, and Luxemburg meet. General Patten is buried in the military cemetery on the way to Luxemburg City.
A Michelin Green Guide-- Germany is more than useful. It tells what to see and where to zig zag across the river for the best scenic views
I'm pretty sure that what I'm going to describe next happens in September as well as in the summer, but you might want to try to check it out although I don't know how as I have never seen it listed in any tourist info or guide book, but there it is. There are a lot of little towns on the Mosel that have brass bands. On Sunday afternoons, the bands set up along the river and play German marches and umpah music while the natives gathered in the park to drink beer.
We hit this once in early October on a Mosel river cruise where we sat on the sun deck and heard 4-5 of these concerts as we slowly went down the river at 14 mph.