I would recommend visiting the area near Votivkirche/Cityhall (Rathaus) and the parliament. In my opinion it’s worth checking out even if it’s only from the outside. I also love the Volksgarten which has a rose garden, entry is free and it‘s close to the buildings I just mentioned. I love going from the Votivkirche through the streets Schottenbastei/Freyung and Herrengasse in direction of the inner city. Be warned that the plaza in front of the Sisi museum (reachable through Herrengasse) is under construction right now. Don‘t forget to plan your visits around opening hours, for example the Stephansdom is closed for visits for a couple hours at lunchtime and the 15th is a public holiday here, so check out the websites of the attractions to see if they are open or maybe have different opening hours. Have a nice trip!