No vignette required if traveling from the north 
If traveling to the hotel by car via Ulm - Pfronten and Munich - Garmisch-Partenkirchen, you do not need to purchase an Austrian autobahn sticker.

Other useful links:
Train schedule for Austria (ÖBB) - http://www.oebb.at/
Train schedule for Germany (DB) - http://www.bahn.de/
Innsbruck Airport - http://www.flughafen-innsbruck.at/
Munich Airport - http://www.munich-airport.de/