BERLIN (3 full days) - Arrive Berlin early evening, stay 4 nights A
visit to a concentration camp would be ideal (we've never been to
Germany). Looks like a trip to Sachsenhausen would take most of a day
(leaving us 2 days in Berlin). Thoughts?
I've done a couple of Germany / Italy trips. There's something really nice about that combo.
And while 5.5 days is skimpy, I think a Berlin / Rhine combo is near-ideal for getting a brief first impression of Germany as well.
But I think what you really need to do is spend all of those 3 full Berlin days right in Berlin. Even then you'll have to leave out things you might want to see/do. I think visitors should ask themselves some serious questions before including Sachsenhausen. IME, the semi-obligatory visit to a German concentration camp has become a misguided practice, especially for such a brief visit. What Holocaust lesson have educated visitors not yet learned? What impressions of Germany and its people will you take home after a couple of hours unearthing once again all the gruesome details? Besides the time involved, there's the condition of your stomach and your state of mind... it will be deeply unsettling at best, and possibly a good bit worse than that for a good while longer than anyone wants. To "Never Forget" is important. But it does not mean visitors must traumatize themselves on their vacations. If you visit any of the many WW II sites in this city, the cruelty of the Nazi regime will already be enough to conjure up the horrifying images that you already have in your heads... so I say include Sachsenhausen only with great trepidation.
It's easy to do Bacharach and maybe Mosel (Burg Eltz?) by train?
Train service here is excellent but you must walk to the castles. Marksburg is your best Rhine Castle visit - an excellent experience - a must see if must-sees exist. It's an intact medieval castle with authentic feel. Take the train to Braubach and walk up from the station in about 30 minutes. Tours in English at 1 and 4 pm.
Braubach
Marksburg Castle
Burg Eltz is an hour's walk each way from Moselkern station. There are buses to the castle on weekends after a train ride to Hatzenport station. It's easy to reach either station, but both the walk AND the bus ride eat up a lot of time (the bus schedule is very skimpy and you will probably have to wait for the next one here or there.) I like Burg Eltz - it's very fancied up and museum-like with furnishings from different periods. But if you end up being pressed for time, leave it out in favor of a visit to Marksburg and Rheinfels Castle (which as you know is right in St. Goar.)
The other good place to visit on the Mosel is Cochem. It's adorable. It's easy to reach as well - the train from Koblenz follows the river the entire way for a very scenic ride. The Bundesbank Bunker is a top attraction. The castle there is no longer medieval, now a reconstructed palace that you can read about here. But it is easy to get to from town (on foot or by shuttle,) the views are spectacular, and the tours are both popular and interesting - and available in English:
https://reichsburg-cochem.de/?lang=en
St. Goar is a good base for these outings. But if you want FREE train trips during your stay, book a room in lovely Boppard, where all guests receive a free "Guest Ticket" to cover their entire stay!