Vienna is compact and not nearly as sprawling as Barcelona. While it ultimately depends on the location of your hotel, the majority of the sites are within the Ring or along the Ring. I can walk straight across this area in about 15 minutes. It is also flat.
There are some sites that are not within this area, such as the Belvedere (not that far anyway from the Ring) and Schonbrunn (definitely not within walking distance). There is also the Hundertwasserhaus, the Sigmund Freud Museum, and the hillside wineries that are farther afield.
As noted above, the public transportation systems in Vienna are easy, clean, fast and very safe. You can easily take a tram up to the Belvedere, Hundertwasserhaus and the Sigmund Freud Museum. For Schonbrunn you take the subway (U4) line direct.
The only places I've ever seen a line is Schonbrunn. I understand, however, that Belvedere is now requiring a timed entry slot, although that line is never long anyway.