Munich and area - help please

You are right to have questions about mountain weather (and shorter days) in late October, but Innsbruck has several valleys just south of it (Zillertal, Stubaital) that could be fun if the weather is permissive, and its a much shorter hop than the Dolomites. They both have good hiking in the valleys and a number of ski lifts that may be operating to go up higher on nice days. But the lifts may be undergoing maintenance between summer tourists and skiers. The same can be said in the Dolomites even if the weather is perfect.

https://www.zillertal.at/en/
https://www.stubai.at/en/

Bohemia in the Czech Republic is a lovely area just west of Prague. It is not not high Alps of course, but very scenic.

The "Fraenkische Schweiz" is the high hilly region north of Nuremberg, which has ruined castles, great bicycling (eBike anyone?) and pretty towns and countryside.

https://www.fraenkische-schweiz.com

For thirty days with a car I would consider Innsbruck, another base near Nuremberg/Bamberg/Bayreuth and around Prague.

typo corrected.

Franconian Switzerland is a nice area and a good suggestion - and to research it, you can try the English term I just provided, or, if searching in German, it should be spelled as it is spelled in the link which NickB provided - not as he has spelled it in quotation marks:

Fraenkische Schweiz

...or if you have a German keyboard... Fränkische Schweiz

The south end of the Bodensee (Lake Constance) will give you access to the Alps and offer plenty of other attractions at that time of year. Why not fly into Munich, head to Bodensee, and fly out of either Paris or Frankfurt?

...or if you have a German keyboard... Fränkische Schweiz

Actually, you don't need a German keyboard if you have a Windows computer (PC). For ä, while holding down the alt key, type 228 on the numeric keypad.
But actually, ae is not just an English workaround for ä. It has legitimate significance for the development of ä, and is recognized by the Bahn websites, as is oe (for ö) and ue (for ü), and their capitalized counterparts (AE, OE, and UE).

As far as suggestions, I agree with Bodensee, and in particular Lindau. And on the way to Lindau, outside of Oberstdorf in the Illertal, Kleinwalsertal is a high Austrian valley worth seeing. To get there, take the train from Immenstadt im Allgäu.

Harburg and Nördlingen, in a part of the Romantic Road closer to Munich, are interesting if you like castles and walled towns.

To the east, there is Berchtesgaden, if you missed it on your Salzburg trip. There is also the medieval castle at Burghausen or the nature preserves in the Bavarian Forest NP.

And, of course, there are Rothenburg odT and Würzburg to the north. All places worth visiting.

October shouldn't be a problem with touring in mountainous areas, except if you want to go up to high altitudes.

Other places to consider:
1)The Romantic Road from Fussen to Wurzburg. It includes several medieval walled towns like Rothenberg ob der Tauber and Dinkelsbuhl. Also, Oberammergau, home of the Passion Play; Augsburg, very historic city over 2000 years old and more.
https://www.romanticroadgermany.com

2) Nuremberg and Regensburg. Both historic cities worth do 2-3 days for both.

3) Vienna- Great city, go to a concert it is great as well as tour the city.

4) Innsbruck is worth a day or two.

5)Also, in the Garmish/Fussen area, do the Zugspitze, highest mountain in Germany.

Kloster Andechs.

Kloster Andechs is a great idea. From Munich, take the train to Tutzing, then a bus to Andechs. It is a steep walk from the bus up to the Kloster. We stop at the Braustuberl on the left for a nice meal at the beginning of the walk. We like it better than the Andechs Biergarten further uphill. The bier at Andechs is also great.

An alternative to the route through Tützing is to take the S8 to Herrsching and the bus from there to Andechs. It's about the same length of time, but the bus ride is a lot shorter. That's what I did.

Thanks Lee, I'll try that this September.