This is a magnificent city full of students and with places worth seeing. I must highlight the beautiful restaurant located in the middle of the river. Mur Island makes reference to the name of the river that crosses the city of Mur.
Murinsel, an island on the river Mur, is a curious and dramatic floating island about fifty meters long with two gateways connected to the riverbank. It is was built in 2003 for the cultural capital of the city of Graz and serves as an amphitheater, a resting place or you can have a drink in the cafe there. I recommend visiting this structure 100%. Although coffee is slightly more expensive than in other pubs of the area, you really should pay the extra. It's a priceless experience.
The Clock Tower (Grazer Schlossberg in German) is located on top of the Schlossberg hill, which is roughly 475m high. At the top of this hill a castle was built finally naming the city of Graz (which derives from the Slovenian word "Gradec" which means "small castle"). The Clock Tower was the only part of the castle that was saved from demolition as ordered by Napoleon in 1809 following the Treaty of Schönbrunn. Since 1839 the Tower and its surroundings have been a public park, designed by Ludwig von Welden. The clock tower has a curious feature, because its needles work differently to most watches. The hands that in regular clocks mark the hours here mark the minutes, and vice versa. This is because originally there were only needles to mark the hours, the minute hand to indicate the minutes were not added until much later. There are two ways to access the top of the hill and both have an attractive quality. One way is to choose to walk up a string of seemingly endless stairs, but its worth it for the extraordinary views of the city and the river Mur. On the other hand, there is a funicular (Schlossbergbahn - Sackstraße http://www.verbundlinie.at/) connecting the top of the hill with the Kaiser-Franz-Josef-Kai. The Clock Tower is, in my opinion, the most beautiful place in Graz A highly recommended place!
Although not as spectacular as other cathedrals from the outside, the interior of the Cathedral of Graz (built in the fifteenth century by Emperor Frederick III) is very impressive. A must-see is the mural of the three plagues (lobsters, black plague and the Turks) in the southern outer wall near the Mausoleum. There is also no charge for admission.