For your visit a day and a half is the right amount of time.
Distances are mostly walkable, but getting to Schloss Eggenberg or to Mariatrost requires usage of public transport.
Worthy attractions: Schloss Eggenberg; Cathedral; Schlossberg.
Left for another visit: Kunsthaus; Katherinenkirche and Mausoleum; Landeszeughaus; Basilika Mariatrost.
Last visit: December 2016.
Graz is recognized on UNESCO World Heritage list as a wonderful architectural ensemble – and it is true, architecture delights await you at every corner.
Things to See
The historic center converges on the dazzling Hauptplatz ♥♥♥ which is dominated by imposing Town Hall. The comparatively wide Herengasse ♥ houses a number of fascinating buildings. The narrower winding and climbing Sporgasse ♥ is another headline street.
Cathedral ♥♥ is well worth exploring. The neighboring St Catherine’s Church is more colorful on the outside and contains Mausoleum with tombs of some of Hapsburgs, but I did not go inside.
Uhrturm ♥, at the edge of the public park at Schlossberg ♥, stands guard over town. Its clock hands are the opposite to what we expect them to be (the smaller shows minutes, the bigger hours), which adds to its quirkiness. From under the tower, you can take in panoramic views over the city. A stairway descending to Schlossbergplatz from the hill offers additional opportunities for elevated perspectives, with benches at many of its landings. If you have time to linger, consider catching the sunset on one of the benches.
Schloss Eggenberg ♥ is away from the city center, reached by tram and then some walking. I was not able to see its interior on account of it being closed for the winter season, but you can walk into its courtyard, go up the galleries, and also explore the gardens year-around (you can also peek through the glass doors for a glimpse of a ballroom when the castle is otherwise closed). Peacocks in the garden provide additional entertainment – there are at least two dozen of them.
I spent a little over half a day in Graz, giving preference to walking over visiting museums, so I did not fit into my itinerary places like Kunsthaus, Landeszeughaus, or Basilika Mariatrost (the latter is located further afield). They remain targets for a return visit.