One of the most interesting things about Vienna is the "ring", the huge circle of linked streets that Vienna built in grand style to create a tramway/motorway to cope with all the traffic when immigration into Vienna exploded in the 19th century. The idea of the ring is that from any point on the ring, you can walk (or take a carriage!) into the "inner city"), so the fast way to get about town is to hop on a tram on the ring and get off at the closest point to what you want to see. However, because building this "ring" came at the height of Imperial Vienna's powers, the "Ringstrasse" is mile after mile of monumental buildings of Imperial Splendor. So one of the more fun things to do in Vienna can be simply to take a Ringstrasse tram and look out the window and see these amazing buildings, plus a glimpse of the Danube and the great parks of Vienna. At some point, you need to get off one tram and switch to another, but you can find this information online.
However, with just one day in Vienna, maybe it is better to focus on the famous things in Vienna, and pick the ones that most appeal to you. Vienna is famous for its historic cafes and elaborate cakes, for its gardens and palaces, for its spectacular art museum (the Kunsthistoriches), for its opera and waltzes and boys' choir plus famous compsers. It is also famous for its Spanish riding school and for the modern art movement of the Secessionists (Klimt, Schiele, Otto Wagner) and famous for being the home of Sigmund Freud.
So if you pick a few things that interest you most, you will find Vienna is a very walkable city, and you will see a lot along the way going to your sightseeing targets.