My itinerary 15 days in Bavaria/Austria.

Not sure of your interests, but I would stay 1 night in Fussen and add another night to Nuremberg. I think you may be shortchanging Nuremberg. The tunnels probably would not be at the top of my list, but it may be your priority.

https://www.thecrazytourist.com/15-best-things-nuremberg-germany/

The one thing about your itinerary is perhaps you have underestimated the time it takes to travel to each city and checking in and out of hotels. Both take up a lot of your time. You have 6 cities in 13 days.

The inside of Neuschwanstein is a let down. Don't expect to see a lot in the interior. The exterior is great and the view from Mary's bridge is scenic.

I have not stayed in Fussen so I am not sure it needs 2 nights.

Enjoy your trip.

I agree with the above. I'd actually skip Fussen entirely, and use the days elsewhere .
Also, with the current airline overall chaos and strikes, give yourself an extra day on the beginning, because you may not arrive anywhere near on time. Our last year's flight to Munich was delayed by six hours, and we arrived past midnight. I'm glad we did not plan to go further that first day.
I love Rothenburg, but you do have 3.5 hours of train travel, with at least three changes, once you're thru passport control. I just wouldn't recommend that on jet lag, unless you're experienced travelers and are confident with your jet lag ability. The last train change is usually only five minutes, with lots of steps. so you need to be sharp. Once you've arrived at the Rothenburg train station, it's best to take 8€ cab to your hotel, as it's a bit of a walk, and the streets confusing on arrival.
That being said , I love being in that town, so keep it on the itinerary. My daughter introduced me to R'burg on one of our mother- daughter trips, and we've returned twice since.
I'm so glad you and your daughter have that time together, and I'm sure you will cherish those memories forever !
Overall, you're going to some wonderful cities, so have a great trip!

https://community.ricksteves.com/travel-forum/trip-reports/san-diego-to-munich-just-getting-there-part-1

Thanks!
We are stopping at Fussen because one of the big things on her list is to see the mountains, and to see the old towns. I think I agree about the tunnels. There are better things to see. I have been looking up train times the whole time, and trying to keep in mind arrival times. I figured that if there is something we don't get to, that is ok. This trip is supposed to be about medieval, castles, mountains, and classical music (bring on the Mozart!). I'm not really sure how I would do it otherwise.

I appreciate the thoughts!

The Alps/lake in Berchtesgaden, outside of Salzburg, are more impressive , IMHO, than those in Fussen. I'll attach my 2022 Trip Report, so you can see how we day tripped to Berchtesgaden on public transportation, it's actually just over an hour by bus.

I keep looking at your itinerary, and it is a challenge to rearrange, I agree, keeping Vienna. And I think you should keep Vienna. Maybe someone here will have a creative approach.

Are you experienced travelers?
Good luck!

EDIT-
I added my Trip Report to my earlier post. Hopefully it may be useful.

I have been overseas a few times (China, Wales, England, Italy, Greece). I am a planner, so I have been researching everything. But I do that so that when we get there, we can relax and go with what happens.

Vienna and Salzburg are biggies for us because I am a professional vocalist (high classical soprano), and my daughter will be graduating with her vocal performance degree. So that is why we are spending more time in those towns.

And I should say that she specifically asked to see the castles, since she grew up a Disney fan. I know that one is not very impressive inside. That's not really the point for her. She wants to see the fairy tale castles. I was thinking of spending the time we are in Fussen almost as a break before moving on to the bigger/busier city.

I wish we had more time to see the other lake you mentioned, but money is a problem. I only have so much saved, and every weekend gone also means I'm not making money at my job. Hoping to go back someday and see the stuff we miss!

A couple of suggestions:

1) Yes, do Rothenberg, but then head down to Fussen on The Romantic Road and see some great medieval walled towns, largely undamaged in WWII. The road ends in Fussen.

2) Also, consider staying in Garmisch and doing the Zugspitze (take cog train or cable car) to top of highest mountain in Germany.

Fussen is actually more of a tourist trap and is an exhausting day because of the hilly terrain and distances between the two palaces. It is the opposite of relaxing. Lots of crowds, standing in lines, no shade, even with timed tickets. ( I guess in that respect, it is like Disneyland.) obviously if it's important, you all will go, but it was a very different experience than I was expecting, (not like what the beautiful PR pictures portray.) Also, check the website, many areas of the interior are under renovation.
As for the musical experiences, you and your daughter will be in heaven in Salzburg and Vienna. Enjoy these fantastic locations!

Day 5: Munich. First, Mass on Sunday. 10am Mass at the Asam

Of course the Asam church is very impressive but you should know that in St.Peter (which you will also visit with the RS audio tour) will be a Latin Mass on Sunday at 10am. Maybe that would be something too?
Only in German but sure will help: https://alterpeter.de/gottesdienste/

Day 6: Munich. Nymphenberg Palace complex. Relax at a beer garden that night?

If you have been to the Residenz then visiting the Nymphenburg Palace is somehow similar. I would go to the park in the morning. I did this very regularly for a while to photograph mostly the animals there early in the morning: https://www.flickr.com/photos/calabrones/albums/72157648888753959

Relax at a beer garden that night?

Yes beer garden is Munich :-) My favorite beer garden in one of my favorite districts in Munich (Haidhausen) is the Hofbräukeller on Wiener Platz.
A real beer garden always means you have to buy the beverages there (there is much more than just beer) but you can bring your own food (you can buy food in the beer garden as well). And very important, it's self-service. But don't worry because Munich is an international city and English will be understood where the beer and drinks are sold. Just find a table where nice people are sitting and ask if you can sit down.

Anything else we might have missed and wanted to see

-Maybe your daughter wants to see the famous Eisbach surfers at the edge of the English Garden? https://www.munich.travel/en/pois/sports-leisure/eisbachwelle

-Or the Olympic Parc and visit the Olympic tower: https://www.munich.travel/en/pois/sports-leisure/olympiapark

-Maybe the younger Munich?
https://www.munich.travel/en/topics/urban-districts/futuristic-nesting-ground-with-history-and-lots-of-life-culture-and-creativity
https://www.munich.travel/en/topics/eat-drink/schlachthof-district-party

I would put the Munich visit at the start, after arriving rather than going to Rothenburg rightbaway. That will change the day you leave if going to mass is a must.

Is there a reason you’re flying into Frankfurt rather than Munich? It would be easier and save you some time if you could fly into the Munich airport.

And where are you flying out of? Since you’re in Vienna, flying out of there on an open-jaw ticket would certainly save you time and money as well.

I will check out the Latin Mass, thanks! Mass those Sundays in non-negotiable.

I had wondered about doing both palaces in Munich. I will ask her about going to the garden instead. That's a good thought.

We are flying into Frankfurt from DC because it is cheaper, direct, and closer to Rothenburg.

We are flying out of Vienna on the way home.

I had followed Rick's advice about deciding where we want to go and making a line from location to location. And I picked the locations after reading his book and talking to my close friend who grew up in Germany and still has most of her family there. I will definitely look at the other suggestions here (they look good!), but not sure how much we can do because of time/money.

I really appreciate all the responses!

We went to Fussen(two nights) because my daughter wanted to see Neuschwanstein Castle. For me, Fussen was the upside to a visit to the castle which I think is a colossal waste of time.

Through reading forums I think people in general have too high an expectation of Neuschwanstein. I've visited twice, in 1987 and 2012, the first time more relaxed and with fewer people. Yes, it's gaudy and excessive, but a reflection of the landlord and his tastes. It makes no sense to me to go out of your way just to snap some photos from MarienBrücke, as some members suggest. Visit Neuschwanstein, Hohenschwangau Castle also (a nice woody interior and folksy paintings).

If Neuschwanstein is a must-do, so be it. But if you’re going there just to see “a castle and mountains”, I will encourage you to drop Fussen and add those nights to Salzburg. Go to the fortress at Werfen (just south of Salzburg) instead.

https://www.salzburg-burgen.at/en/hohenwerfen-castle/

With the extra day in Salzburg, you could go to either Berchtesgaden or Hallstatt. You will fall in love with the Salzburg area, and find there is much more to see than you have time. Spending more time in one place also gives you some flexibility in case of bad weather.

Fussen is nice, and yes it has mountains nearby... but don't go there for the mountains if you're gonna head to Salzburg. As mentioned above, the Alps near Berchtesgaden and Konigsee are MUCH more impressive.

First of all, you can't go wrong with any of your chosen locations! Rothenburg is a good first stop as it is smaller and easier to manage than a large city. Try to take the walk (described in the RS book) outside the town walls and along the river to Detwang. There's a biergarten along the river that is peaceful and scenic.

Fussen can be busy, but it has a charming pedestrian area. I don't know your travel style or stamina. If you're up for it, there are walking paths in the Newschwanstein area. Those photos you've seen of travelers with the castle and bridge in the background? There's a shuttle bus stop near that spot-just walk downhill a bit instead of following the crowds up the hill.

If you want to make one less hotel change you might consider going from Rothenburg to Munich (add a night here), then visit Nuremberg as a day trip (arrive early/stay late?). You may feel that is too little time in Nuremberg....

While in Salzburg try to visit the Hellbrunn Palace with its trick fountains. You can get there by city bus. In Salzburg-anywhere, for that matter-keep your ears open for organ music as you walk near churches. I've managed to hear some impromptu "concerts" when my timing coincides with an organist's practice time.

Fussen is a lovely, wealthy little city. Perfectly fine place. But if you want to see big Alps and stay in Germany go to nearby Garmisch-Partenkirchen. Fussen isn't really a mountain town, more like at the base of the foothills. From GP you can see and go to huge mountains with a lift network and nice mountain huts. It's much more "Switzerland-ish" than Fussen.