Just after Leibnitz go through Gralla to the east untill you reach river Mur and then follow the cycling route 2 which goes along the river to Graz (and possibly further). It is very well marked and some sections go through nice residential areas.  Mostly car-free.

After the long ride you can cool yourself in Schwarzlsee and have a rest before you go back. :)

On the way back, the route on this map uses local roads with less and slower traffic, going through villages and countryside.