24 Days in Germany - Itinerary Thoughts?

Berlin to Nuremberg is faster and much easier by train than by car. Will you be in Nuremberg whilst there? Or surrounding? Parking not especially easy nor inexpensive in Nuremberg.

Consider getting the car when you leave there.

Great plan. When I lived in Augsburg, Germany I hiked up from Garmish to the top of the Zugspitze twice. It is a two day hike and great.
Check out staying in the Fraundorfer hotel in Garmisch.
Also, The Romantic Road from Fussen to Wurzburg is great, with cities like Rothenburg ob der Tauber, Dinkelsbuhl, Donauwirth, and Augsburg.
https://www.romanticroadgermany.com

Honestly, there's very little you use for a car. Save the hundreds of Euros and treat yourself. The train lines for that whole trip are great.
Nuremberg, I quite liked the tour of the Art Bunkers. Wasn't able to get an English one the day I was there, but they provided me with an audio device. Also enjoyed a beer bunker tour there. Just walking around the innerstadt is a quite nice day. The old Zeppelin Field and Parade Grounds are fascinating for history buffs. The museum at the Kongresshalle may be back open, too.

You'll be near Bamberg -- I HIGHLY recommend a visit there. One of Germany's great beauties. About 1hr by the S-Bahn.

Garmisch is one of my favorite places. You have LOADS of great hiking at your doorstep (relatively speaking). Partnachklamm can't be missed. The Höllentallerklamm is amazing, as well. If you are fit, and up for an adventure, you might even book nights in huts and make your way all the way up to the Zugspitze over a few days. Otherwise, you can totally just take the train/cablecar up. Enjoyed dinner at the Frauendorfer hotel.

...2-3 nights in and around Rothenburg ob der Tauber...

As long as you are that close, a visit to Wurzburg to visit the Prince Bishop's Palace is something you should consider. And while in the Garmisch area, you might want to visit Oberammergau which is very close by. You should be able to google each and them and see if they hold any interest for you.

Parking not especially easy nor inexpensive in Nuremberg.

Thank you for your reply, Nigel! We are thinking to stop in Leipzig on the way to Nuremberg. We have been going back and forth about whether to rent the car or not. We will spend one day in Nuremberg and maybe explore the near by town on the way back (when we drive from Rothenburg ob der Tauber to Berlin).

Great plan. When I lived in Augsburg, Germany I hiked up from Garmish to the top of the Zugspitze twice.

Thank you @geovagriffith! The Fraundorfer hotel looks really cool. However, we decided to rent an apartment in Garmisch for the week so we can cook our meals.

Do you have any recommendations for smaller hikes near Garmisch? I am also wondering if we are spending a week in Garmisch, should we cancel the 2-3 days in Tegernsee and instead spend those days in Salzburg and berchtesgaden. Thoughts?

Honestly, there's very little you use for a car.

Thank you @jwells6. Do you think we will be okay without a car in Garmisch and Tegernsee? We plan to explore near by areas of both the places, may be Innsbruk and/or Berchtesgaden?

And if we do not have a car, is there a good way to drive the romantic road?

I’d get the car as you leave Nuremberg. You need a car for the Romantic Road properly

The bus network in Garmish is great. I've never needed or wanted a car there. If you're wanting to drive to more than just Rothenberg, maybe try to pick up a car after Garmisch. I don't have a ton of info on that, as I've kinda just stopped at a couple of the towns here and there by train.

I like the amount of time you are giving each place.

I think Tegernsee offers more contrast to Garmisch than Berchtesgaden would. I adore Berchtesgaden, but I think I would go for the lake experience at Tegernsee over another mountain experience if I was going to spend a week at Garmisch.

Leipzig is a great city, especially if you have interest in the events that led up to the fall of the Berlin Wall. It's great to visit Nikolaikirche there. I happened to be there in 2019 for the 30th anniversary of the Monday Demonstration that preceded the Fall of the Berlin Wall by a month way back in 1989.

Another city along your path that I like a lot is Erfurt. I actually like it better than Nuremberg. It avoided the bombing that Nuremberg received in WWII. It has a lot of gorgeous Fachwerkhäuser (half-timbered houses). It may be worth a gander, unless WWII history is
a major priority for you on this trip -- then you should definitely go to Nuremberg.

Another little gem not too far from Bamberg is Bayreuth. They have an incredible Opera House there called the Margravial Opera House. They also have an Eremitage a bit outside of town. The buildings there are all decorated with small stones which makes it look soooo cool. We didn't get to do the New Palace or the Richard Wagner Museum, we were tuckered out from walking the gardens at the Ermritage. Also we were there on a Sunday so not a lot was open shopping wise, so it is on my list of places to go back to.

While in Bamberg if you are into beer, check out their smoked beer which they are famous for. Shopping in Bamberg is also very fun, I may or may not have spent way too much there.

And one more consideration would be the Harz. Very close to Berlin, and visiting places like Quedlinburg or Wernigerode might be right up your alley. Beautiful nature and good hiking, too.

Having no car there is stiill good train connection from Nuremberg to Tegernsee
One change at Munich Central Station and one hour each from Nuremberg to Munich and Munich to Tegernsee

There are boats on t he Lake Tegernsee to get from one village on the Lake to the other

https://www.seenschifffahrt.de/en/tegernsee/timetable/timetable/

and also the mountains are in reach with the Wallbergbahn from Rottach Egern on the Lake

https://www.wallbergbahn.de/en/summer/summer/

Bus connection from Rottach Egern center to the cable car station Wallberg

https://www.ipp.mpg.de/1535497/9556Tegernsee_Kreuth.pdf

From Tegernsee to Garmisch again via Munich with train 2,5 hrs one change
Tegernsee Munich 1 hr Munich Garmisch 1,5 hrs

my point of view:

You can do all your travel by car or by train but I would do the first part from Berlin to Nuremberg to Tegernsee to Munich by train
and get a car in Munich then drive to Garmisch for a week do all the excurions you like by car from there and go to Rothenburg along the Romantic road by car return the car in Nuremberg afterwards and return to Berlin again by train
For me it would be the most comfortable way to travel this route

Check the possibilty and prices for oneway car rental Munich Nuremberg
Should be around 600 to 750 Euros for 10 days

For train travel I would choose the Interrail One Country Pass Germany 5 travel days for one month
around 220 Euro pp there might be offers during Euro24

Thank you for all the replies, so helpful!

I could use some advice on another question. On our way back, I am thinking of staying in Wurzburg for 3 nights instead of Rothenburg ob der Tauber. And plan to do a day trip to Rothenburg from there. Apart from spending time in Wurzberg, we'll also spend time in Bamburg on the drive back to Berlin.

Is staying in Wurzberg a good plan for three nights to explore these areas or should I stay in Rothenburg ob der Tauber?

Personally, I would prefer to stay one night in Rothenburg and two nights in Wurzburg.

I'd fly to Salzburg (or Munich). Then train to Garmisch, train to Nuremberg, and fly back to Berlin. You can rent a car locally if you want, or use the public transportation. And that way you're not backtracking where you're already been. Driving to Berlin from anywhere near Nuremberg is going to cost you an entire day of your trip each way.