Advice needed for trip to Berlin and Saxony

Short time frame for that plan - normally you could spend alone 5-6 nights in Berlin, especially as lover of classical music and of churches - btw my father built a new Catholic one in Berlin. And believe it or not: Berlin Cathedral is a protestant church - they offer the 19th organ summer this year (pipe organ with 113 registers!).

Hotel Park Inn Alex offers the best view to west overlooking the eastern center. Tip: rooftop terrace.
Tip: Hotel Motel One Berlin-Upper West in western cente offers unique view on memorial church and short way to station Zoo which offers connections to sites. Ask for access to upper floor terrace.
Hotel Riu Plaza Berlin in western center offers also views from high floors.
Hotel Telegraphenamt has a very rooms with view but not high floors.
Avoid Gendarmenmarkt which is currently a construction site.

The club areas are neither in eastern or western center. One classic rainbow quarter would be close to Riu Plaza.

At your date of travel do not miss Festival of Lights in Berlin.

Tip for the organist: a short visit at Musical Instruments Museum (Potsdamer Platz) would offer the unique chance to see and maybe hear a real Trautonium - I place a bet he had never heard of the instrument although likely heard the sound of it when watching Hitchcock's "The birds" because the sound of the aggressive birds was a Trautonium.

If you want to rent a car do this directly before leaving Berlin - if you do not know the city a car is no advantage.
For renting and driving a car in Germany ensure validity of your driving license and care for IDP if you have a driving license from a US state (mandatory by law).

We also enjoy spending time outside enjoying natural beauty!

Since you will be already close have a look at Saxon Switzerland.

Bach lovers with more time I would normally recommend to visit also Lübeck's St. Marien Church because young Bach (before he was a super star of his time) was travelling there - unallowed for four months (!) - to learn from organist master Buxtehude on one of the best instruments of this time. Lübeck was a very rich town for hundred of years - its merchants spent very high amounts of money for their main church.

For ancestry research in Königshain-Wiederau you can contact the Kreisarchiv Mittelsachsen. Better contact before journey.

We’ve been to all of the cities you’d like to visit with the exception of the ancestral town mentioned. I hope you’ll follow up on MarkK’s link to see if you can get more information about his ancestors before you visit the town. I did this for my family a few years ago and it yielded information and current relatives, more than I was hoping for.

In regard to your interests and 7-8 day time limit. I’d recommend after arrival in Berlin, taking the train directly to Wittenberg for 1-2 nights, take a train to Leipzig for 3 nights and then take the train back to Berlin so you can also visit Potsdam for 3-4 nights. There is so much to see in just these cities, well connected by train, that I don’t think you’ll have time on this trip for many side trips. We were so fortunate 2 years to be in Leipzig for a national choir competition where every street corner, passageway and church were filled with impromptu and formal performances. Leipzig is really a delight and music filled city. Check out all bulletin boards at church entrances for normal organ concerts as many churches across Germany have guest organists for weekly performances.

In Berlin I like all of the recommendations MarkK gives for hotels! In Leipzig we stayed at an OK hotel near the modern train station as there were so many choirs in town during the three days we were there in 2022.
I hope you both have a great time.

Are you flying from the US for this short visit? Berlin, for example, is a very rich destination, especially in October as opposed to August. Berlin has (historically, anyway) three Opera houses, and a lot of music performances. You are not even allowing enough time in the cities you have selected.

I mean, after you find an indoor pay-parking garage, the Bach museum will take you over an hour. If you are really lucky, you might hit a choir rehearsal in Bach's own church. You will not have time for another important church, St. Nicholas , which was crucial in the fall of the Soviet Union. You don't have time for the excellent art museum, or the trail of Goethe. As a New Yorker, the Gewandhaus concert hall was important to me because Kurt Masur (from Leipzig) directed the NY Philaharmonic.

Have you considered Weimar, Erfurt, the UNESCO WHS Dessau-Worltiz Gartenreich? I don't see that you have the time to visit the Grunderzeit Museum just outside Berlin, founded by the subject of the Pulitzer Prize play, "I am My Own Wife". There are enough important museums (including the Military History museum, which requires a U-Bahn ride) in Dresden for a few days. At least one of the "Green Vaults" is hopeless without a well-in-advance reservation. There are other Bach cities, like Weimar and Eisenach.

With that little time (half days only) for Wittenberg and Leipzig you can barely scratch the surface. In Wittenberg you will be able to see the main sights from outside at least, walking down the main street. And maybe you can pop into a church and visit one of the museums. But Leipzig ... The Bach house (museum) plus St. Thomas and St. Nikolai churches (where he worked) alone will require three hours minimum including the walk between them. And along that walk (pedestrian zone) you will see a couple of other worthwile sights like Mädler Passage (historic shopping arcade with the famous restaurant Auerbach's Keller, featured prominently in Goethe's Faust), the Renaissance town hall (city museum), the art museum (Museum der Bildenden Künste) ...

Anyway, spend an hour or two in Wiederau for ancestry research and the rest of the day plus the next one in Dresden. Dresden has enough things to see and do to keep you busy for a couple of days - Frauenkirche, Zwinger, Royal Palace, State Art Collections, catholic cathedral, Brühl's Terrace, a paddle steamer ride on the river ...

As for accommodation in Leipzig and Dresden - booking.com has lots of options. A quick search came up with some hotels in your budget that I can recommend: Star G Hotel Premium Altmarkt, Holiday Inn Express Zentrum, Aparthotel am Zwinger, and some that are slightly above your budget: Amedia Plaza, Holiday Inn, Premier Inn Prager Straße ...

You might consider Motel One, a German chain hotel with very comfortable rooms (and beds) and very reasonably priced. I stayed at the one near the train station, and found it to be a good location (a block or so from the station) but secluded enough to be quiet and easy to get to. I think I paid around $120 for a double room, and sometimes they can be cheaper. There are other locations in Berlin as well. https://www.motel-one.com/en/hotels/berlin/