Rhine, Moselle, Rothenburg ob der Tauber...... and Heidelberg? or Nürnberg? or Stuttgart? Munich?

What time of year? Don't miss a Strassenweinfest, which take place in various towns on the week ends, especially in September. This site has an event finder and other info: http://www.mosellandtouristik.de/en/

Thanks Sam!

I wouldn't bother with Nuremberg, Heidelberg, or Rothenburg. I would fly out of Frankfurt as well. If you want an ultra-quaint touristy village, the Mosel has Bernkastel.

It's also worth visiting Traben-Trarbach if you want to see some Jugenstil twentieth-century architecture.

The Mercedes museum in Stuttgart is excellent, but the Porsche one is less interesting unless you are a huge Porsche fan.

Stay in St Goar for a couple nights at Hotel Reinfels for $80 with a picture
window on the Rhine...take the best boat ride on the Rhine just outside your
door down to Bacharach and train back...Great castle and outdoor deck for drinks above town.

"We want to go along all of the Rhine and all of the Moselle."

That's not hard on the Rhine for the area between Bingen and Koblenz (the most scenic part.) Train tracks and roads cover both river banks. On the Mosel you will spend endless hours in the car if you attempt the whole thing. Better to bypass most of the numerous river bends west of Cochem if traveling by car. By train, Koblenz-Cochem follows the river. Koblenz-Cochem-Trier by train takes you to many nice towns on the way.

If wine figures in your plans and you're driving, that will require some serious scheduling (DUI blood level limits are low.) By train, you have complete freedom to do some tasting and traveling around at will. Wine tasting is typically done in town - not out in the vineyards - so don't feel the car will mean better access to tasting opportunities.

Boppard wine garden, in town, near station:
http://www.deutschlandgourmet.info/bilder/gross/5710-Restaurant-Weinhaus-Heilig-Grab-Boppard.jpg

Anyway... I would encourage you to be selective on the Mosel about your river destinations. Cochem is a good base town there.

I agree that St. Goar makes an excellent base town on the Rhine, especially for train travelers.

I suggest making Mainz a stopover upon leaving the area for Heidelberg or Stuttgart or Nuremberg or wherever you are headed next. 4-6 hours in Mainz is probably adequate. There's a lot to see, but you probably won't be interested in seeing everything. Mainz is not "quaint" for the most part, however.

Neither is Koblenz, which IMO ranks somewhat lower than Mainz as a destination.

https://www.tripadvisor.com/Attractions-g187393-Activities-Mainz_Rhineland_Palatinate.html

The ship ride from St. Goar to Bacharach, though heavily promoted by Rick (why only this tiny piece is a mystery?) allows you to see only 2-3 castles. Do the whole Rhine Gorge, from Rüdesheim/Bingen up to St. Goar to see all of the castles.

Visit Oberwesel, just north of Bacharach. Walk some of the town wall and visit the Liebfrauenkirche - the reddish church near the train station

I second (or third) the recommendation to stay at Rheinhotel in St. Goar. Email Gil and ask for the balcony room with the view of the river. It's not luxurious, but it's a million dollar view. We sat on the balcony with a bottle of wine and saw the most amazing double rainbow appear over the castle on the opposite bank. Magical. Gil said stuff like that happens there all the time.