Trip to Austria in June

Fussen is southwest of Munich where Salzburg, Hallstadt and Vienna are east quite a distance. You would be spreading yoirself out pretty far for the limited time you have.
If you have never been to Munich, you made missing great city worthy of a 4;day visit.
I have been to Fussen, and it is a very small place. There are other regional travel sights I would rather spend my time visiting.
With the time allotted, have you considered visiting Munich and renting a car as you left town. You could drive down to Fussen as then drop over the mountain into Western Tirol. You could take in the incredible mountains going west toward Innsbruck. Then you could drive North and catch Salzburg. From there, you are just a couple of hours from Munich where you fly out of.
I have made this route a number of times and cherish my time in The Alps. It is an efficient place to travel.
Vienna should be saved for your next trip.

I do think this is rushed. Some people like it, some don't. I would personally drop Vienna, but if you want to keep Vienna in this itinerary, I would head there first from Munich and work my way back to Munich.

Yes, it does seem a little rush and a quiet a bit of driving. You will find, no matter how long Google maps or your GPS calulates your trip time will take longer, due to road work and traffic conditions. A three hour trip may take 4 to 6 hours. I ran in to this, when I took my family on a simular 13 day trip, last June. We flew in and out of Munich and used a timeshare in Maria Alm, Austria for 6 days as a hub to see Salzburg, Burg Hohenwerfen, Legoland Germany and Neuschwanstein. The remaining 7 days was used driving around German to see friends in Koblin, Gottingen, Berlín and back to Munich.
Yes, at times we felt rushed and as the driver sometime I was nervous on narrow mountain roads and crowded highways. GPS will help detour around road delays, but the detours added time to the initial trip. Inspite of it all it was a great trip.
My best suggestions are, rent the smallist car your confortable spending time in. Set your cars GPS to English and learn how to use it before leaving the garage. Lastly, do what will make your trip most memorable and enjoyable.

ViaMichelin estimates the driving time from Vienna to Munich at nearly 5 hours, and VM is thought to be optimistic. I would under no conditions want to make that drive on the day I was due to fly home from Munich. Way too many things can go wrong on the road. (And I would try it by train, either.)

Thank you everyone for your input! Based on suggestions, I think we'll remove Vienna. Here's what I'm thinking for a revised itinerary and would love thoughts on whether this would be a better place:

2 nights Munich
2 nights Garmisch or Mittenwald
1 night Heiligenblut or Zell am See
1 night Hallstatt
3 nights Salzburg