4 days; 5 Nights on the Rhine

IMHO. That should be plenty of time! If it were me I would spend one of those days on the Mosel seeing berg Eltz, Cochem and Beilstein.

"Will we have enough time to do this and still see castles along the Rhine, including Burg Eltz?"

Burg Eltz is near the Mosel; as Jill suggests, Cochem is a good destination - it could be combined into a single day trip with Burg Eltz.

Many visitors enjoy a cruise to get an overview of the many castles (and vineyard-clad hillsides, and towns). It takes about 1.5 hours if you start in Bingen and end in St. Goar, which covers the most scenic part.

Burg Rheinfels (St. Goar) and Marksburg (Braubach) are the most accessible castles - and very worthwhile. Rick has a page on these and Burg Eltz: https://www.ricksteves.com/watch-read-listen/read/articles/three-rhineland-castles

So perhaps you combine a cruise on Day 2 with a visit to Rheinfels. On Day 3, Eltz + Cochem. On Day 4, Marksburg, Braubach + Boppard. Day 5, Bacharach, Oberwesel + the ancestral villages.

So yes, I could see Day 1 making a trip to somewhere else. Rothenburg wouldn't be my pick (too far, too touristy) but it's feasible with a long drive there and back. It's also a lot like the old-world wine towns you'll see in the Rhine/Mosel area in terms of style (half-timbered buildings, old town walls and towers...)

There are numerous good options closer to the Rhine and Frankfurt if you want to see something a little different...
TRIER
MAINZ

Following this thread! We are also staying on the Rhine in Boppard for 5 nights and 4 days. Looking forward to the advice you are given!

IMO, Rothenburg is nice but is not worth the effort to get there, as there are plenty of nice towns along the Rhine that are worth your time. I would not base in Bacharach which is also very nice, but so small in comparison to St Goar, for example. Definitely worth a visit, but can be walked from end to end in 15 minutes.

I believe St. Goar and Bacharach are roughly the same size, but I agree that St. Goar tends to make a more convenient base town. The ferry crossing, the presence of Rheinfels castle right in town, and the fact that St. Goar is a logical place to end a river cruise... all of these are solid advantages.

We probably could take the trains, but there are small towns near
Bacharach that we want to visit to see areas where our ancestors
lived.

Have you explored the possibility of getting to these places using buses. Use the German Rail (Bahn) website to find schedules.

Thank you everyone for your replies. We picked Bacharach as our base because it's close to some villages/towns where we wanted to do some ancestry research (Oberdiebach, Manubach, Genheim). However, we don't want the ancestry part to the be the focus of this trip so we are open to your suggestions. We will be meeting up with our tour group in either Mainz or Frankfurt on Day 6, so we will need to end up near that area.

Based on comments, it does seem like it might be better for us to base ourselves in another town. We'd still like to stay a couple of nights in Bacharach though because it seems like such a lovely, quiet town. My husband and I like the idea of a laid-back atmosphere because we will be spending 11 days after visiting the Rhine on a whirlwind tour of the Luther lands (Frankfurt, Eisenach, Erfurt, Eisleben, Wittenberg, Potsdam, Berlin, Dresden, Leipzig, Flossenbürg, Nuremberg, Augsburg, Munich).

Russ, are you suggesting that we base ourselves in one place (other than Bacharach) and then venture out each day for the excursions? I will heed your suggestion in skipping Rothenburg! I like the intinerary you suggested, although I think Trier might be a bit out of way. Is Mainz worth some consideration?

Lee, we have considered taking a bus, but we'd like the flexibility of coming and going without adhering to any strict schedules (we have the rest of our trip for that!). Normally we rely heavily on the train/bus systems overseas. My thought is that driving in this area won't be terribly stressful, but maybe I'm wrong about that! Thoughts?

Danke

"Russ, are you suggesting that we base ourselves in one place (other than Bacharach) and then venture out each day for the excursions?"

Actually, with 4 full days, I just sort of assumed you would be making such excursions from Bacharach. I like St. Goar and Boppard a little better for location and logistics, especially for train travelers like me. It's more central. But outings are doable from Bacharach as well.

"We'd still like to stay a couple of nights in Bacharach though because it seems like such a lovely, quiet town."

It's a lovely town. It's fairly quiet in some spots, but the position of the town so close to the tracks has made for a whole lot of upset visitors (and townfolk.) The Kranenturm Hotel is one of those that gets huffed and puffed at with passing trains: http://www.rhein-zeitung.de/cms_media/module_img/1195/597502_1_arslideimg_597502_1_org_bacharach.jpg

The town is wedged between the cliffsides and the railway:
https://upload.wikimedia.org/wikipedia/commons/8/81/Bacharach_Luftbild_01.jpg

Train noise can be avoided to some extent if you choose a Bacharach location carefully - the Blücherstrasse locations just up the little valley, near the church, don't get so many complaints. Check the reviews carefully if you want to stay there. Noise is not unique to Bacharach but it's generally worse there than in St. Goar and Boppard. All the towns are subject to road noise and some river boat noise as well.

I like staying right in town myself. With a car, you might want to scout around for a location outside of town in the hillsides for more peace and quiet. This winery/hotel outside Oberwesel is just an example, not a personal rec.: http://www.gasthaus-stahl.de/hotel/?lang=en

"Is Mainz worth some consideration?" The sights and museums in Mainz are interesting, and it has a huge pedestrians-only zone for shoppers and sightseers.

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

Mainz' open spaces are nice too - the Market Square,
Augustinerstrasse, the main pedestrian artery through the old town, Mainz' Stadtpark are all nice spots. But it's nothing like Rothenburg, if that's what you mean/what you want.

An outing I didn't mention is the one to Bad Sobernheim for the Open-Air museum there - you really get an interesting look at what life was like for locals in recent centuries at this place. Here's the museum homepage. Bad Sobernheim means an outing up the Nahe River Valley, where there are some other towns you might like, including the gem-town of Idar-Oberstein and Bad Kreuznach, with its cute old town and bridge houses.

Rather than the 3+ hours it would take to get to Rothenburg, you could travel just one hour outside of Frankfurt to Büdingen. Medieval, walled town that has never been bombed (unlike Rothenburg which lost 40% of its' buildings). It doesn't have souvenir stores though (or tour buses) and it is wise to book a private tour from the TI as they take you inside the city walls and up on top of the massive towers.
Add in a visit to the neighboring town of Gelnhausen as you need to switch trains here anyway.
http://www.buedingen.info/en/

Thanks everyone for your suggestions. Based on comments, we decided to stay three nights in Boppard and then two nights in Bacharach.

Does anyone have recommendations on renting a car? Is it best for us to rent one at the airport in Frankfurt? My initial thought was to take the train to Mainz and then rent a car (thinking that getting out of the city would be best). Boppard does not have a car rental facility, so that's out.

"Is it best for us to rent one at the airport in Frankfurt?"

It's best not to drive in unfamiliar territory after a long transatlantic red-eye flight (jet-lag, drowsiness.)

You can take the train to Boppard. Some are direct trains - 11:23 (direct,) 11:29 (1 change,) 12:37 (1 change) 13:23 (direct)

Then the next day or whenever, you can take the train into Koblenz (direct, 15 minutes, €5.85) and pick up a car at the station there.

Emmelshausen is also a town where you can pick up. Getting there from Boppard is an easy and interesting little train trip - the steepest tracks in Germany. The trip costs €4.70 and 24 minutes. And that way you don't have to negotiate your way out of the "big city."

Train to Boppard: At the FRA Regionalbahnhof station, use the ticket machine to buy a RMV ticket for two (under €10) to cover FRA-Mainz. Also buy a "Rheinland-Pfalz Ticket" for two. It's a day pass for the trains to cover Mainz-Boppard (€29.) If you are on a direct train from FRA to Boppard, there's no need to get off in Mainz.

I've made two trips to the Rhein-Mosel region, one for four complete days (5 nights) in Boppard, one for three complete days (4 nights) near Cochem. One day I visited the Marksburg, another day St. Goar (Rheinfels), KD boat, Bacharach, Oberwesel, one more day Koblenz and Deutsches Eck, last day, the archaeological sites around Boppard. On the Mosel, one day I visited Bernkastel and Zell, another day Beilstein, one day in Cochem - the Reichsburg and a winery (it was late in the year and Burg Eltz was closed). In retrospect, Beilstein was a mistake because I did it on a Sunday, when the buses ran only sparsely, and I had to spend four hours in a one hour town.

So, neglecting Beilstein, I spent a productive six days in the area. I don't think 4 full days is too much. Do Rothenburg some other time, when you are closer.

Oberdiebach and Manubach are next to each other, a less than 20 bus ride from Bacharach. Genheim is about the same distance from Bingen. You could do it the same day as a cruise from Bingen to St. Goar.

A cheap 4 hour trip that you may consider is taking the "ring tour" in Rudesheim. For about 15 euros you start with a cable car ride over the vineyards in Rudesheim which offers amazing 360 views of the Rhine and surrounding areas. The cable car drops you at the German Unification monument (it has a long German name that I can't recall). From there you walk 30 minutes on a well cleared and marked trail to a chair lift (think ski lift) for a scenic ride into Assmanhausen. Assmannhausen is a nice little town along the Rhine, plenty of half timbers buildings and some good places to eat. From there you take about a 40 minute boat ride on the Rhine past a gorgeous castle back to Rudesheim. The entire tour takes about 4 hours and I highly recommend it!

Speaking of preserved walled towns that don't suffer from tour buses vomiting thousands of day trippers onto it's winding streets, another option near the Rhine that rarely gets any attention is Ahrweiler. It sits in a lovely wine valley a few kilometers off the left bank of the Rhine, and features much of the same types of preserved buidlings and defensive structures that you would find in Rothenburg, but a tiny fraction of the trinket shops.

Burg Eltz is awesome - partly because of the setting. This seclusion makes it a bit tricky to find, but the effort is worth it. Take a tour to learn the stories about the place - charming.

Just got back last night from Germany, We traveled by train from Amsterdam to Cochem and stayed 2 nights at Pension Gundert. Hiked to Burg Eltz and rented bikes and rode along the Mosel to Beilstein. Thanks to Russ and Lee on this forum the trains where easy to use. Stayed 2 nights at Hotel zur Loreley in St Goar before flying out of Frankfurt. Took ferry from St Goar across river to St Goarshausen then train to Braubach for hike to Marksburg castle going past lots of cute old buildings on way to castle. Could not see much of Rheinfels castle, most was closed the day we where there. Walked part of the town wall in Oberwesel but the town was dead at 5pm, lots of closed or empty shops. Took the train one evening to Bacharach from St Goar for dinner, we had a nice dinner but I'm glad we decided to stay in St Goar. One thing I noticed at all small towns we visited along the Mosel & Rhine in the evenings the tourists looking in the windows of all the closed shops, the shop keepers are missing out of $$$.