A member of our family had only a day and night to spend in Vienna. What to do in such a short time?
If you are limited to downtown (the Inner City), a favorite restaurant is Brezel Gwolb (Lederhof 9 between Judenplatz and Am Hof). They serve old-fashioned Austrian country food that is filling and excellent.
If you are interested in a heuriger (winehouses in the vineyards of the Vienna hills where local vintages are served), Weinhof Zimmermann, which overlooks the vineyards in Neustift am Walde. (http://www.neustift-am-walde.at/h-zimmermann.htm) is a stand out. You see more Viennese than tourists at Zimmerman. To eat like a local, mix your wine with soda water, and try the topfen knoedel, a sweetened dumpling with a cream cheese filling for dessert.
For sightseeing, there are two trams that circle the Inner City--one goes clockwise, the other counter-clockwise and on both you end up backwhere you started. You can see the Rathaus (City Hall), Stattsoper (Opera House), Votivkirche, Hofburg Palace, the Danube canal and lots of other sights (even hop off at TGIFriday's), all from the comfort of a tram. If you want the real Sacher tort, its birthplace was the cafe at the Sacher Hotel in the heart of the city.
With a little time on your hands, explore the sidestreets in the downtown area around the Graben. There are some great antique shops, including ones that deal in sports, fishing and hunting, and others that specialize in jewelry (one of the best pawnshops in Europe is the state-sponsored Dorotheum, a warehouse of treasures).
If you would like to see some royal apartments and can't make it to Schoenbrunn palace, Sissy's apartments in the Hofburg are an easy (two hours at the most) tour. Don't do the silver and china exhibit unless you are very interested in seeing lots of silver and china.
If you like military history, Vienna has one of the best military history museums in Europe. If you are short of time, you can see the highpoints in two hours. Look for the car in which Archduke Ferdinand was riding when he was assassinated, a huge mortar from World War II, and a Turkish Army tent from the siege of Vienna to name just a few exhibits. You can get to it by taking a tram to the Sudbahnhof and walking a short distance. Their website is http://www.hgm.or.at/eng/.