Bacharach (Rhine) or Cochem (Mosel)

I prefer Cochem to Bacharach. There's more town to explore, more to do overall, and more accommodations choices. You can tour Reichsburg Castle (right in town) and catch a falconry show there; there's also a cool chairlift ride to a lookout point. The half-timbered old town is very special. And the scenery around town is decidedly more dramatic, IMO.
Cochem's market square
Be forewarned that there are lots of tourists in Cochem. They tend to be mostly European (Germans, Dutch, Brits.)

Bacharach does have some very fine half-timbered buildings. But thanks to R. Steves' resounding endorsement, this very small town is also blessed with a disproportionately large contingent of North American visitors that carry his book around. So if you are looking "...for something very German, quaint and different", then I should tell you that Bacharach often feels more tourist-heavy than other towns. For "very German" on the Rhine, I'd look at some other villages instead - most towns get plenty of tourists, but in some cases not so many - and mostly Europeans. Boppard and Oberwesel spring to mind. Boppard, actually, would allow for day trips both to Cochem and to Bacharach with some ease. Boppard is also closer to Bremen than Cochem or Bacharach.

Boppard street scene
Boppard tea house
Boppard riverfront
Gedeonseck terrace overlooking Rhine and Boppard (short walk from top of chairlift)

Oberwesel town wall
View of Oberwesel

That’s a tough one. Both areas offer up a lot of sights and other villages close by to explore. As for the trains and schedule I can’t comment. I've not done the trains in Germany, so you’re on your own on that one, or hopefully someone else can comment with that. However, I will say that if it’s easier to get to Bacharach then I'd head there. You'll have more time to explore, especially if you take an early train the day you head out. I've been to both areas, but have explored Cochem and not Bacharach (that was more of driving along the Rhine and observing the sights, so I didn’t explore the town itself). I know I didn’t help you all that much, but I hope I at least nudged you in a direction.

I can't comment on Cochem because I didn't get there on my trip. I did stay in Bacharach, which I loved, but only for one night. I visited Boppard by boat and I really enjoyed that town. I like Russ's idea of staying in Boppard and visiting both of the others as day trips by train/boat - it really makes sense, then you could enjoy 3 wonderful towns in the region.

WOW Boppard looks great. I'll look into it.

Dot

I prefer the Mosel as everything is smaller and cuter. Departures from Colmar take about 5 hours and a few need only 2 train connections, so those would be first choice. It's worth it!

Boppard is both a central location for travel and a beautiful city. If you want to spend some money, there is a line of hotels (Best Western Bellevue, Rheinlust, et al) on the street facing the river. If you want to spend less, there are some smaller hotels, gästehäuser, pensionen, and Privatzimmer farther back. I spent 5 night there 10 years ago in a single room in a private home for 25€ per night.

Boppard accommodations: You'll find numerous options at booking.com and other online engines. But for the best selection take a look at the town website, where you'll also find a large number of family-run B&B's / Guesthouses and apartments ("holiday flats".) The price Lee paid in Boppard is a good one; you can probably find something in that range for 2015 as well if you look at the pages below. Note that September is wine festival month - ALL these small towns fill very quickly on weekends - and you should book early for the best choice.

Some places can be booked online using the Boppard website, others by email (or other) request. Boppard accommodations: Click on a choice at the left; for online booking choices, once you reach the blue search box, select "English" at the top and enter your dates and other info. Boppard has numerous "suburbs" so to be in the center, select "Boppard, (Boppard, Romantischer Rhein)" under "WHERE". When your room options pop up, there may be links to the host's homepage (if any.)

Just for fun and for an example of what you might find... I did a search-and-book for October 15-18 and found a 2-bedroom apartment or "holiday flat" - Ferienwohnung Hartenfels - available in Boppard's old town, steps from everything and a flat, reasonable walk to the train station for outings. 3 nights, €133.50 total for two persons (which I guess works out to about €22 each per night, without breakfast of course.) There was no website listed but googling "Ferienwohnung Hartenfels" located both the homepage and a listing at a commercial website called "Holiday Insider", which is in German but which contains reviews in English and some photos. A handful of reviews rate it 4.8 of 5 stars.
FERIENWOHNUNG HARTENFELS at Holiday Insider

The Holiday insider page has an availability calendar for the Hartenfels place; September is already beginning to fill - there are fewer available days in September than in August or July.

Hartenfels homepage (German) (Although it's only in German, the apartment owners do speak English, according to info at the Boppard town website.)

We spent three nights in Bacharach and loved it. As a note, on our way to our stay on the Mosel in Zell (which we loved), we stopped in Cochem and couldn't wait to get outta there. Massive amount of tourists compared to Bacharach. Huge tour buses disgorging people. Full of all sorts of touristy souvenir shops. It didn't feel nearly as authentically German as Bacharach. We tried to go up to the castle and see the falcon show but my legs gave out, we felt lost...and then we discovered that there's a bus going up right from the center marktplatz. One thing you can do on the Rhine is take a river cruise - which isn't easily offered on the Mosel. We walked to the DK Ferry from where we stayed at Pension Winzerhaus. We had a nice ride to Goar where we hopped off and spent the day wandering the town and exploring the Castle Reinfels ruin (we walked to and from downtown and we're over 60). We had dinner at the very picturesque Altes Haus in Bacharach and had a wine sampling tray and snacks next door at Weingut Fritz Bastian the next day. We walked a back street to find a path through the hilly vineyard to a spectacular viewing tower and the best photo spot ever. Compared to Cochem, Bacharach is very small town, loaded with charm and appealed to us more. There's plenty to love about Cochem, it's just bigger and more touristy.