Moderate-Strenuous Day hikes &/or overnight hikes

The Osterreichischer Alpenverein is the hiking association in the Austrian Alps. You can use the drop-down menus under "Hutten" to search different regions and see the huts that are there. Unfortunately their whole site is in German BUT you can join the Austrian Alpine Club UK and get the same information in English!
As you leave Munich and head east, past Salzburg, toward Vienna the land flattens out and there aren't any mountains. But south of Munich and Salzburg the Bavarian Alps are beautiful!
We have not hiked hut-to-hut in Austria or Bavaria but we have done so in France and Italy. Wonderful experiences! If you join the UK version of the association you can make reservations and get discounts on staying at the huts. I'm sure they have suggested routes as well but I will leave that to someone who has hiked in Austria as I have not!
Good luck!

We have not hiked in Austria but I am looking at the Zillertal. You can get to Mayrhofen by train and trails up to huts start there. You might be able to work out an out-and -back to a hut for an overnight. Two hut nights would be better.

The Berliner Hütte is reputed to be a classic.

http://www.mayrhofen.at/en/sommer-urlaub-ferien-familie/berlin-high-trail/

Linda:

Been in the Alps a lot so I know that hut-to-hut hikes exist all over the Austrian Alps. I would suggest choosing a mountain range or area of interest and then going from there.

For example, here is one in the Dachstein region:
http://www.hallstatt.net/about-hallstatt/active-summer-holiday/wanderzeit-en-US/mountain-huts-and-alpine/adamekhuette-adamek-hut/

Five hours, seems to start near Lake Gosau which is very beautiful and then you can check the website for hikes to other huts from Adamekhuette. Or use the contact number. I have stayed in Gasthof Gosausee (lovely location but busy) - maybe you could use that as a base?:

http://www.gasthof-gosausee.at/Willkommen

I don't have personal experience of hut-to-hut hikes as I am not up for long hikes like that.

Between Vienna and Munich, the land is flat. You'll have to veer off course significantly. I'd go south once you reach Salzburg, towards the Dachstein.

As others have posted, you will need to make a detour to find anything with good views. You don't mention time of year, which matters quite a lot.

Oetscher is a superb trip. You can access the Oetschergraben by rail (Wienerbruck), walk up the valley, go up the Raherkam (it's a scramble with some exposure although you don't need a rope but be careful of weather -- lightning is a hazard), over the Oetscher summit to the hut and sleep there (long first day). Day two you can hike over to Gemeindealpe on what is basically a ridge walk, and walk down lift down to another rail station in Mitterbach. There is a spectacular new hut on Gemeindealpe where you can have lunch. I have done this in the fall and it's gorgeous that time of year. There are some steep sections in both days, so you will feel that you got your money's worth. :-)

Maybe this site would be useful:
http://www.salzburgerland.com/en/spiritual/pilgrimage-routes.html
Several very long routes, but you can certainly segment them.

Hochschwab might also be good.
http://www.regionhochschwab.at/index.php?option=com_content&view=category&id=29&Itemid=112

Be careful to check that huts are open on your dates and make sure you have insurance coverage for a rescue. The rescue crews WILL charge you and a helicopter ride out of the mountains is pricey.

We have an English speaking section of the Alpenverein in Vienna and our past events are archived. You might find some good ideas here:
http://www.alpineclubvienna.org/archivedevents.php
If you open the trip sheets, there will be info on transport, huts, etc.

Be safe and have fun!

Thanks for the comments so far.

For season, this will be June.

And to clarify, I do know there's nothing exactly on the way--I mostly mentioned where I'm coming from and going to so that I didn't get suggestions that were way off from that route. But a 3-4 hour train ride between Munich and the location and the location and Vienna is totally doable. So no worries on what's been suggested so far!

Basically, I'd like to find an area comparable to Muerren in Switzerland, but in Austria, if possible, since Austrian Alps works better with my overall trip plan.

Zonderpaard, the Oetscher trip sounds amazing? How would the snowpack be in June do you think? Passable?

June is normally fine up there. Trade fall color for wildflowers. :-)

Have you considered self-guided options? Utracks has some good harder hikes in the region if I recall: http://www.utracks.com/index.php?pfsys_tripsearch_index=0&module=we_trip_search_results&country=139318&activity=&grading=&date_from_day=&date_from_month=&date_from_year=&date_to_day=&date_to_month=&date_to_year=&pfsys_tripsearch_submit|value|submit|value|.x=23&pfsys_tripsearch_submit|value|submit|value|.y=8

I think that's good because they transport your luggage.

Most of those though are week-long... Wanderweg Holidays has short overnights to huts too.

I hope that helps...