I spent 6 days in Vienna, with a day trip to Salzburg and another to the Wachau valley and Melk Abbey, and had no trouble filling my time. I enjoyed it so much I'll be back in April for another 3 days. My main focus the first time was mainly about the sites featured in my favorite movie, The Third Man. I also made a point to be there on a Saturday to visit the Flohmarkt (flea market), which is part of the Naschmarkt and fun if you enjoy funky old foreign things like I do.
To me, Vienna is right up there with Paris when it comes to a multitude of great museums, so if you enjoy art, particularly of the Secession era, don't miss the Leopold & Belvedere. This trip I'll be going to the Kunsthistoriches and possibly the Military museum, along with re-visiting the Leopold. You might also enjoy a visit to the Prater and a ride on the Riesenrad.