Vienna, hands down is my most favorite city in the world. It just such a city of details, and unexpected experiences. The last time I was there, during a casual walk after dinner, we stumbled upon Friday mass concert at St Thomas that was absolutely transcendent. That kind of thing doesn’t happen in other cities! St. Stephen also always has beautiful contemporary art exhibits in the very traditional gothic setting.
Two things to check when go to city: your manners and the hours. People in Vienna are extremely courteous and expect you to be the same, and most of the shops close after 6 and all day Sundays. t
Mozart Cafe is the most touristy and central cafe, but I recommend the very bourgeois Landtmann or the quaint Kleines, walk over to the Crown Jewels, and buy the package ticket with the Kunsthistorisches Museum (aka Art History). You need a full half a day for the Kunsthistorisches Museum and it’s sister museum Naturhistorisches Museum. Check out the Klimt’s in the ceiling in the lobby, and learn more the fascinating history behind these two museums.
Don’t worry about which of delicious restaurants to pick from at Naschmarket for lunch, since much of the cooking comes from central kitchens. However, Neni is one of my favorites, event though the food is Middle Eastern. Get your fill of spices, and cheese at Naschmarket as well, but remember that most of the vendors only accept cash. From dinner, stuff yourself on a weinerschnitzel larger than your face at Figlmuller with the waiter who looks like the Austrian father from the Sound of Music.
For those psych or history geeks, Sigmund Freud’s house and it's subsequent Nazi occupation is a very interesting exhibition (but there's limited occupancy so you do have to wait up to 30 min in line, plan accordingly). On a nice day (which is basically every day) in Vienna, stroll around upper or lower Belvedere (which the vodka is named after!). But if you want the palace of palaces, Schoenbrunn Palace about an hour outside the city. The Österreichische Nationalbibliothek has a breathtaking collection of books (unfortunately you can’t read) and ancient prints, complete with secret passages behind the bookshelves.
If you visit past September, the local vintners set out tables for tasting, simple foods and gorgeous views in the 19th district. Feuerwehr Wagner is highly recommended–well designed interiors of wood and wine presses, with blankets for chilly nights and the best Schnitzel outside of the city center.