First of all - all opening times, admission prices and contact details can be found in the links:
We start directly in Mürzsteg at the Appelhof family hotel (https://www.muerzeroberland.at/ausflugsziele-naturpark/ausflugsziele-im-naturpark/spielplatz-appelhof/) opposite the imperial hunting lodge (now the summer residence of the Austrian Federal President, not open to the public) and briefly follow the Mürztal cycle path R5 to the Holzknecht Museum (a 5-minute drive from Mürzsteg). After a visit to the museum (https://www.muerzeroberland.at/ausflugsziele-naturpark/ausflugsziele-im-naturpark/holzknechtmuseum/), things get sporty.
Keeping to the left, the route climbs up to the Falkensteinalm (gravel road) and, after a scenic rest, continues into the so-called ‘Tirol’ (named after lumberjacks from Tyrol who worked here many years ago).
Here we reach the Mürz valley again and follow the cycle path out of the valley to Neuberg an der Mürz. The minster (https://www.muerzeroberland.at/ausflugsziele-naturpark/ausflugsziele-im-naturpark/muenster-neuberg/) , the nature museum (https://www.muerzeroberland.at/ausflugsziele-naturpark/ausflugsziele-im-naturpark/naturmuseum-neuberg/) , the Kaiserhof Glasmanufaktur (https://www.muerzeroberland.at/ausflugsziele-naturpark/ausflugsziele-im-naturpark/kaiserhof-glasmanufaktur/) and of course numerous catering establishments make a stop here almost obligatory.
At Teichwirt Urani, about 2 km in the direction of Mürzzuschlag outside the centre of Neuberg, our path branches off to the left and leads us, cycling briefly uphill towards Schneealm, but keeping right before Michlbauerhof, to the Forest of the Senses (https://www.muerzeroberland.at/ausflugsziele-naturpark/themenwege/wald-der-sinne/).
After a walk through this unique forest, we cycle briefly back to the road that leads up to the Schneealm. Keep right and cycle uphill past the Michlbauerhof until you reach the so-called ‘Öd’, which is quite steep. Here we do not continue on to the Schneealm but keep slightly to the right downhill to the ‘Hanslagrabner’ farm and to Altenberg an der Rax.
There we visit the small, fine Montanarum (https://www.muerzeroberland.at/ausflugsziele-naturpark/ausflugsziele-im-naturpark/bergwerksmuseum-montanarum/), a museum on the history of mining in the Altenberg valley, right next to the Altenbergerhof inn. Incidentally, the unique Austrian climate change trail (https://www.muerzeroberland.at/ausflugsziele-naturpark/themenwege/erlebnisweg-klimawandeln/) and the Montanrundweg (https://www.muerzeroberland.at/ausflugsziele-naturpark/themenwege/montanrundweg-altenberger-erzberg/) also start here.
After a visit to the museum, we return from here and cycle out of the valley to Kapellen with the world's largest spinning wheel (https://www.muerzeroberland.at/ausflugsziele-naturpark/ausflugsziele-im-naturpark/spinnstube-kapellen/) and from here along the Mürztal cycle path R5 into the valley again to Neuberg an der Mürz. We follow the R5 further up the Mürz to Mürzsteg, our starting point, where we can make a short stop at the tunnel cinema in Krampen (approx. 15 minutes' walk from the cycle path) (https://www.muerzeroberland.at/ausflugsziele-naturpark/themenwege/schauberger-triftanlage/).