whilst in graz we visited the schloss eggenberg (eggenberg palace) which is on the edge of the city (it is easy to reach on tram number 1 if you are interested!).
on the sunday we visited it was free to enter the grounds and we enjoyed wandering around the corridors of the palace and the lovely gardens. it was really peaceful and felt like you were in the heart of the austrian countryside despite being only a 10/15 minute tram ride out of the centre of graz. i would definitely recommend a visit if you are in graz and have a spare couple of hours!