Itinerary help - Garmish, Berchtesgaden or both?

Question- why are you flying out of Salzburg? Most folks here would recommend flying out of Munich, since you have so many more flight options, and the train ride is about two hours.
I love Salzburg, especially the evenings and mornings, so I would vote to spend a few nights in the old town.
I love Berchtesgaden and would encourage you to spend some there- you will get the Alpine experience. The beauty is incredible.
Have a wonderful trip!

With only 6 nights for both Munich and Salzburg, I would skip Garmisch.

We stayed at this lovely apartment near Hallein, just south of Salzburg, in 2018 with our two teens. https://www.booking.com/Share-3AppQc

You would need a car if staying at this apartment. You can take the train or bus into Salzburg in 20 minutes, or park in Salzburg pretty easily. There’s a huge parking garage built into the hill where the fortress is. We stayed for 5 nights and spent 2 days in Salzburg, 1 day in Berchtesgaden (45 min drive), 1 day in Hallstatt (1+ hr drive). We did the sommerrodelbahn near Hallein twice. It’s on the way to Berchtesgaden.

I would give yourself more driving time than google maps says. Traffic can be really bad around Munich. There is often construction on the highways during the summer.

We went paragliding over Salzburg with FlyTandem. I can’t recommend it enough. They also fly over the alps near Werfen (40 minutes south of Salzburg) which would be amazing. You would take a cable car up and float down. Werfen is stunning, with a great fortress and ice cave, if you want to make a day of it there.

I'm a bit partial to the Zugspitze, since I lived near there for a few years. But Neuschwanstein is not near there. It's another hour away.
Berchtesgaden is less than a half hour drive from Bad Reichenhall if you just want to day trip from there. Note that both GP and Berchtesgaden are tourisy in the summer.
Likewise, Salzburg is a similar length of time by car, but I wouldn't recommend bringing your car there and dropping it (in Austria). You would likely be facing a very substantial drop off fee for doing so in a different country than you picked it up. Plus you would need to buy an Austrian vignette for the car if it didn't already have one.
If you want to sightsee in Salzburg (and IMO you should if you've never been there before), then I'd recommend dropping the car near the border (Frielassing immediately jumped to mind, if it has a rental office for your rental company), then taking the train to Salzburg. Take a taxi to the airport.

As for accommodations, you might consider getting a Ferienwonung. These are vacation apartments in Germany, often attached to a private home.

Pickup the rental car as you're leaving Munich. If you return the rental car in the same country as it came from, you'll avoid paying return fees. And Munich Airport is a very good one to fly through..

We usually would go west out of Munich and then turn south going toward Garmisch--stopping along the way. Our destination is usually Innsbruck--making day excursions up on the mountainsides from village to village. The Alps there are incredibly beautiful--about 100 mi. south of Munich.
Then we wander over toward Salzburg--about a 2 hour drive. It's one of the more friendly cities you'll ever find.
You can easily find places to stay in the region. As a major ski resort area, accommodations are everywhere. See Booking.com and/or AirBnB.com. I often go to Google Maps and click on the Hotels icon at the top--and hotel icons pop up everywhere by the price.

Go to the Königssee. Take the electric boat. Hike to to Fischunkelalm on the Obersee. Enjoy the view. Maybe Leogang or Steinplatte for less touristic Alpen areas?

Garmisch in the winter. Berchtesgaden in the summer.

Munich with teens could be fun. I would go for:

• Olympic Park (maybe possible to climb the roof) https://www.olympiapark.de/en/tours-sightseeing/guided-tours/roof-climb/
• Take a view from the Olympic Tower
• Visit BMW World and Museum (close to the Olympic Park anyway)
• Check out Allianz Arena (Iconic home of Munich's soccer club) https://allianz-arena.com/en
• Check out the Eisbach Surfers in the English Garden https://www.munich.travel/en/pois/sports-leisure/eisbachwelle
• The kids like Street Art? Then visit Werksviertel Mitte or Schlachthofviertel https://boredinmunich.com/street-art-in-munich/

I would suggest to decide first in which area you want to stay Garmisch or Berchtesgaden. Your time is very short and therefore I would either choose one or the other. Berchtesgaden is much more to do and it is close to Salzburg.

"worth seeing the Zugspitze if we're not interested in Neuschwanstein"

Zugspitze is not close to Neuschwanstein and therefore can't answer this question. Zugspitze is Garmisch, Neuschwanstein is Füssen

"Are the summer driving times I'm seeing on google maps realistic with traffic?"

I would add some extra time in summer

"If flying out of Salzburg would you just stay outside of Salzburg and take a day trip in, or drop the car early and stay in the thick of it."

I would drop the car in Germany. In Salzburg a car is anyway a burden. From Berchtesgaden to Salzburg it is only a very short train ride

"accommodations for family of 4 (with separate beds for kids) outside of the touristy areas near the Zugspitze"

I thought you want to stay near Bad Reichenhall?

Heck, I didn't know Salzburg even had an airport.

OK, you have four nights in Salzburg. Berchtesgaden is nearby, so don't miss spending a day there and go to The Eagle's Nest, the view is awesome.

Salzburg is great, visit the castle up on the hill, the cathedral and Mozart's house. Perhaps take the Sound of Music tour. You can do that easy in two days. That leaves you one more day, but getting to Garmish (117 miles) is over two hours one way.

The Zugspitze is a great trip, you take the cog train or the cable car and there is a glacier on top of the mountain. Some people ski in the Summer. Still, I would not plan on all that travel for a day trip.

Speaking German is not required, but learn a few phrases.

Thank you all so much for taking the time to respond. This is all very helpful!

It was actually less expensive for us to do a multi-city flight and fly out of Salzburg rather than Munich.

With the way the trip is shaping up we're looking at 2 nights in Munich - 1 night TBD - then 2 nights in Bad Reichenhall, 1 night in Salzburg. My main question is where to put that TBD night...drive down to the Zugspitze, stay near Berchtesgaden, add another night in Bad Reichenhall or somewhere in-between.

It sounds like the weather in June in the mountains can be very unpredictable?
There are so many great suggestions here - I very much appreciate the insight.

Bad Reichenhall and Salzburg are way too close together to switch hotels. I’d suggest all four nights in one central place.

FWIW we stayed 5 times in Ramsau bei Berchtesgaden. Total of 18 nights. It’s maybe a 30 to 40 minute drive to Salzburg. 10 minutes to Berchtesgaden and just a few more to Konigssee. The alpine scenery in the Ramsau, Berchtesgaden area is amazingly beautiful. The Rossfeld Panorama Road above Berchtesgaden is a gorgeous drive in the alps. The Jennerbahn is a cable car trip next to the Konigssee boat trip. There are also luge rides, sommerrodelbahns in the area. You could stop at Mad King Ludwig’s Herrenchiemsee Palace between Munich and Salzburg/Berchtesgaden area. The Wolfgangsee is also only about an hour from Berchtesgaden area.

We stayed five times at the Pension Mayringerlehen in Ramsau bei Berchtesgaden.

Paul

"2 nights in Munich - 1 night TBD - then 2 nights in Bad Reichenhall, 1 night in Salzburg. "

Sounds like you will spend your whole vacation with changing hotels and packing suitcases. This will be no fun I guess. I would suggest 2 nights in Munich and 4 nights in Berchtesgaden.

Things you could do in and around Berchtesgaden:
Day trip to Salzburg by train
Check out Bad Reichenhall and visit the salt mine and a spa
Hike through the Wimbach gorge or the Almbach gorge
Visit Lake Hintersee and Ramsau
Check out lake Königssee by boat and visit St.Bartholomä and lake Obersee - hike from there to the Fischunkelalm
Take the cablecar up to the Jenner mountain
Visit the Kehlsteinhaus/Eagles Nest
Stroll around Berchtesgaden

https://www.berchtesgaden.de/en/home
https://www.berchtesgaden.de/en/nature-wonders/gorges
https://www.berchtesgaden.de/en/nature-wonders/hintersee-lake-and-ramsau