Munich/Bavaria/Vienna - Family with older teens

Tegernsee is a good option for a daytour from Munich 1hr away

Oberstdorf and Berchtesgaden with 2hrs each are a long drive for a daytour

I would choose one of them as a base for some nights if I want to go there.

Oberstdorf and nearby Kleinwalsertal are good places for hiking
The Kleinwalsertal is an Austrian Valley which can only be reached from Oberstdorf /Germany
We stayed in Hirschegg at the Suitehotel Kleinwalsertal and
in a Holiday Appartment in Mittelberg

Here some info on the Valley Kleinwalsertal

and two videos about Hiking in the Valley

Hirschegg to Wildental

Baad ins Bärgunttal

Its a 2hrs drive from Munich City Center

Hi - we're a group of 8 (4 adults then 14/12/9/9) going to Munich & Salzburg about the same time as you, with some similar interests mitigated by the age of the kids. Not sure what your plans are for lodging but I'd recommend locking that down pretty quickly for Munich/Bavaria. Euro '24 is happening in Germany while you're there; may be easier as you're likely getting 2 double rooms and we needed places to fit 4.

Assume you're looking for opinions here - given that they will be jet lagged when arriving in Munich they won't get to experience much there before crashing that evening. If the focus is really on the mountains why not just get the travel over with and go ahead to an Alpine base? We looked at Fussen (if Neuchwanstein is a must) then G-P, Mittenwald and Innsbruck before deciding to go to Salzburg because of proximity to Berchtesgaden area for hiking/biking and ease of transportation. It was really a coin flip. Even though the public transportation is amazing, I'd still aim to limit that (so Munich as a base wouldn't work). That would also play into how you're getting to Vienna and how long that will take. I do think people have more patience for transportation time than I do, so take that into consideration.

Also - depending on budget I'd highly recommend looking at the Wellness spa hotels in whatever Alpine location you choose as your base - you can find them that make the hiking/biking easier - and we haven't experienced anything in the US like them. Just be aware of the lack of clothing in the spas, depending on where you choose. A number of them provide basically every meal and the food is likely very good so factor that into the cost.
Not where you're going but the one we've stayed at previously is: https://www.gmachl.at/en/ (no kids on that trip)
And we're staying at https://www.laschensky.at/en/ this trip to give you examples.

Belgium, Germany and Austria are all great (Brussels is meh but everywhere else I've been is great) so enjoy the trip.

everyone is very excited about the mountains and views (we live in
Iowa, so mountains are a novelty!). Ideally, we would take cable car
up a mountain, day hike to hut for lunch, and seeing some amazing
vistas.

No, you don't want to stay in Munich for 3-5 days.

Mittenwald is my favorite town for those preferences. There are trains that leave Munich at :32 after the hour and you'll reach Mittenwald in less than 2 hours. The Bayern Ticket day pass covers this journey - €29 for one person + €10 per additional person. Please read about the lifts, river gorges, etc. at the page below:

https://hastingshouse.typepad.com/hastings_house_us/2007/04/mittenwald_germ.html

As the map shows, there are trails you can take once you reach the top of the Karwendelbahn lift:

https://www.gemeindewerke-mittenwald.de/fileadmin/bilder/BZW/Lift/panoramakarte/Panoramakarte.jpg

Mittenwald's location makes an outing to Innsbruck, Garmisch-Partenkirchen, The Zugspitze, Oberamergau, and Linderhof Palace quite easy by public transport:

https://bahnland-bayern.de/files/media/bahnland-bayern/tickets/regio-ticket-bayern/Regio-Ticket%20Werdenfels/beg-gr-gueltigkeitsbereich-regio-ticket-werdenfels-2021-05-ansicht.jpg

Maybe this place near Reutte would suit you too:
https://www.tripadvisor.com/Attraction_Review-g580114-d7372839-Reviews-Highline179-Reutte_Tirol_Austrian_Alps.html

After dropping bags in Mittenwald on the 27th, you might want to backtrack that afternoon to Garmisch-Partenkirchen... not because Mittenwald doesn't have restaurants - it does - but because the Fraundorfer Inn offers a Bavarian evening, and your family still has a valid day pass for riding the trains that day, which gets you to G-P and back to Mittenwald for no additional charge.

https://www.youtube.com/watch?v=XD8SvqNDZxE

Fantastic advice from everyone! We have secured our hotel in Munich for Days 1-2. After much searching, I booked a VRBO in Garmisch Partenkirchen for 4 nights (Days 3-6), which will allow us nearby day trips to Zugspitze, King’s Castles, and day hikes. This looks like a great fit for our family. We will travel to Vienna on Day 7.

I now need advice with transportation. My idea is to rent a car in Munich on day 3 to take us to GP, and then return the car before we travel to Vienna (by train?).

1) What is the easiest/best way to rent a car in Munich on Day 3 if we are staying in Old Town and then heading south? I don’t want to rent at airport because we won’t use it on days 1-2.

2) What is the easiest/best way to return car (do we need to go back into Munich?), and how best to sync this up with train to Vienna (we have not bought train tickets yet – can this be done the day of the trip, or should we pre-buy?)

I'll be taking basically the same crew (cousin w/ son (18) and daughter (16)) through Bavaria and then to France two weeks ahead of you. We are basing out of Garmisch for 3 days and I plan to show them some of Munich, the Zugspitze and Partnachlan, and then either Innsbruck or the castles; depending on what they choose. You should consider hiking down from the Zugspitze if the weather's nice. (If it's cloudy don't even bother going up.) Do be aware that the weather can change quickly in that part of the world, and be prepared for rain.

You can probably get buy without a car, depending on what you're using to travel by train. Both the Deutschland Ticket and the Bayern Pass will give you access to he busses and streetcars, along with the underground in the cities. In Vienna you'll need the local ticket. If you do feel you need a car rent one from Sixt in Garmish and take the train there from Munich. (Unless you have to stop along the way in Oberamergau or Ettal.)

Salzburg isn't all about music, frankly I've never made it a focus of the multiple times I've been there, but if you are a history buff it's worth a day or two. Still, Vienna is one of my favorite cities. Make sure you visit the Kunstmuseum, and if the guys are into military stuff the Military History Museum. The hunting and fishing shops are Springer Erben (because being from the mid-west I'll assume this is of interest.) The worlds oldest pawn shop is still in existence, it's called the Doretheum.

In Vienna, plan an evening at the City Hall Film Festival
www.visitingvienna.com/entertainment/events/rathaus-film-festival/
Melk is a great idea (I have only done train, the bike and boat options looks fantastic).
Ride the Ferris Wheel in Prater at sunset then go to the Schweizerhaus Beer Garden (if you didn't know, both of your children are of legal drinking age in Vienna).
And, before you leave watch The Thrid Man, a movie about post WW II Vienna. It was filmed in Vienna and you can see/tour some of the movie locations.

I wouldn't rent a car for the Gapa stay. Places reached easily or fairly easily by public transport: Partnach Gorge, Hollental Gorge, Zugspitze, Eibsee, Ettal Abbey, Linderhof, Mittenwald, Innsbruck, Oberammergau (and good alpine coaster), Murnau/Staffelsee. Free transport with visitor's card provided by landlord?

There's a lovely, eays trail from Garmisch to Hammersbach; nice lunch at the hotel there.

We've visited Neuschwanstein twice, many years apart, when we stayed close by. I wouldn't go out of my way for it now. But, if it's a must.....If you do make the effort, do see it, not just take a photo from the bridge. If you are up for it, walk across the bridge and up the hill for about 20/30 minutes for a different view of the castle/palace.

Train to Munich from Gapa about 6.5 hours, one or two changes.

We've never stayed overnight in the Munich core but have made a few day trips. Our most enjoyable day was spent at Nymphenburg and its gardens.

Car rental: The location of your VRBO may or may not lend itself to easy access to the rail and bus systems. I'd consider that first.

As previous advice indicates, some destinations (including lovely Mittenwald) are generally easy to reach and FREE as well (with one of the available guest cards that come gratis with your rental.)

Garmisch-Partenkirchen > Mittenwald: 30 minutes, Bus #9608

Garmisch-Partenkirchen > Oberammergau, Ettal Monastery, 25-40 minutes, Bus #9606

Oberammergau > Ludwig II's Linderhof Palace: 30 minutes, Bus #9622

Map for these routes: https://bahnland-bayern.de/files/media/bahnland-bayern/tickets/regio-ticket-bayern/Regio-Ticket%20Werdenfels/beg-gr-gueltigkeitsbereich-regio-ticket-werdenfels-2021-05-ansicht.jpg

Free bus rides to the Partnachklamm and other destinations closer in on bus lines 1-5:
https://www.gw-gap.de/images/stories/vb/2019_05_04_gap_linienplan_04-19_a4_2.pdf

Getting to GAPA is quite easy by train from central Munich. 1.3 hours by direct train, €56/4 using the Regioticket Werdenfels day pass. Note that this day pass is valid for unlimited journeys that same day... so you could drop your bags in Garmisch and then proceed wherever you wish by train within the Werdenfels travel zone. (Mittenwald would be an obvious option.)

So... assuming that your rental has a convenient location for doing SOME but not all outings by train or bus, you could postpone picking up the SIXT car in GAPA until maybe the last day of your stay there. Use the car for outings that are otherwise inconvenient. Then head toward Vienna via FREILASSING (Germany) where you can drop the car without penalty and begin your train sequence to Vienna.

Another option: Use public transport to and around GAPA, then pick up the car in AUSTRIA (Innsbruck is a short train ride from GAPA) as you proceed toward Vienna. You might actually find it handy to hit the Wachau Valley by car on your way to Vienna (as opposed to backtracking there from Vienna on a day trip.) This way you pick up and drop off within Austria (and thus avoid foreign drop-off fees.)

Tip collection for kid / teen places in Bavaria and Munich.

I would stay at least a full day or two in Munich. There is so much to do there and they have some wonderful city tours and beer/brewery tours-I don't know if you drink but you must try some beer in Bavaria.

They also have some wonderful museums-like the Deutsche Museum and I liked the Alte Pinakothek for art. And just stroll around or riding bikes through the Englisch Garten-don't miss the surfers and the beer garden.

We did a similar trip (just included Salzburg & Hallstatt as well) at the exact same time of year in 2018 when my kids were 12 & 14. The trip up the Zugspitze was a highlight, something my kids still talk about. I strongly suggest taking the shorter cable car down to the glacier from the top; we almost didn't do it, and afterward we were sooooo happy we did! We had waited for days for the weather to clear at the summit, and it never did, but we had an amazing time anyway. We combined that experience with a lovely boat trip on Eibsee.

Because your family enjoys the outdoors: We enjoyed a lovely easy hike to a waterfall in Farchant, just north of Garmish. At Schonbrunn, my kids liked exploring the beautiful gardens much more than touring the palace; the view from the Glorietta is spectacular.

Vienna is wonderful, but you have not listed Salzburg with neighboring Berchtesgaden, Germany. Also, Garmish/Fussen with all its castles and the Zugspitze, the highest mountain in Germany.