A local tourist office will be able to give you a list of numbers and guide to locations. Maybe even call a few in the areas you are interested in. Some of the staff can be really helpful so put your best smile on and be cheerful with them and you'll probably get what you want/need. If you just expect them to sort you out you may be disappointed. Once you have the lists just choose your route and then select the appropriate hutte or whatever they are called. (I call them all Refuge or Refugio in the Dolomites.) Call and see if rooms/bunks are available. Sorted! Should be available at that time of year. Keep some extra numbers/plan Bs in case you choose a different route one day. Keep the numbers/details safe as you would your maps etc. Fantastically rewarding holiday. Gutte reisen (sp?)
Edited to add:
I would recommend this area:
http://en.wikipedia.org/wiki/Karwendel
http://www.karwendelgebirge.com/
Very good film:
http://www.youtube.com/watch?v=ps5PbzyXuJc
Mittenwald might be a good place to start. Can go town to town there or hut to hut. Very pleasant Alpine scenery and a varied landscape.
Train goes direct from Munich to Mittenwald. Nice route and is only about 2 hours. (Beware work on the line sometimes... Deutsche Bahn rail website will tell you (if you read fine print) if you need to get a bus at any point. If you do is well-run. May add on 10/20 mins to journey. It is a very nice journey even if you need to do a few miles by replacement bus. Probably wont have to though.)
There is accommodation in the nice little town or I hiked out for several hours and got to this place.
http://www.jugendherberge.de/en/hostels/search/portrait/jh.jsp?IDJH=246
it was very suitable for the needs. amazing views and you can eat well there plus drink well. grab beers from the relax-room and just note down what you had and pay the next day. yes there may be children there too but is worth that for the location and views.
The German Alpine troops train there in that area. Quite a few targets set up and we found a lot of very fresh (used) 5.56 blank.