Start by riding the Nordkette cable car network up to the Hafelekar and then get hiking. The walk doesn't need to begin with a trip up to the Hafelekarspitze peak but it's only a 10 detour and well worth it for the excellent views. The line drawn here goes over the peak but it's simple enough not to bother with it.

Drop down off the peak and follow the clear path which hangs high above the Inn valley and follow it east underneath the Gleirschspitze. This traverse beneath the Gleirschspitze is amazing, with epic views and the path constantly winding in and out of tiny valleys so that it never feels tedious.

Shortly after passing under the Gleirschspitze there is a short climb up to a col, from where you drop onto the north side of the Nordkette ridge. Once on the north side the hiking becomes a little more challenging and there are some sections of scree and the path is steep in places. Follow the path as it heads due north and then climbs up to the Mandlscharte col, from where the Inn valley is visible once again.

Drop off the col and follow the zig zag paths down almost to the Arzlerscharte col before heading north-northeast on a gorgeous path path down to the Pfeishütte itself. The hut sits beneath some towering Karwendel limestone peaks and is a traditional Tirolian hut, with a long and fascinating history. It also serves the usual array of excellent, hearty Austrian food and for most hikers, getting their hands on some of this is more important than studying the history of the hut when they first arrive! Once you've refuelled, take the time to study the artefacts around the hut.

Hike south-east out of the hut and climb up to the broad Thaurer Joch col. Descend down a steep and at times narrow path through ever thickening forests to reach a jeep track. Turn left on this to reach the lovely Thaurer Alm hut in a couple of minutes. Grab a quick drink and then make the deceptively long descent down into Thaur village, from where an excellent bus network connects you with Innsbruck.