Vienna is famous for its café culture, and there are coffee houses all over the city, many of which have outdoor terraces that are popular in the summer. Visit them for coffee of course, hot chocolate and pastries. Most famous is Sacher-Torte.
Austria has also some first class wines, mostly whites, slightly on the acid side. Wine can be drunk pure or mixed with mineral water, called "G'spritzter" or "Spritzer". The best place to do so is at the "Heurigen" in the suburban areas of Vienna. Originally the "Heurigen" was open only in summer, but more recently you can have your "Spritzer" throughout the year with a little self-served snack.
Soft drinks: Austria has also a national soft drink called Almdudler. It is lemonade with herbs. Other typical Austrian soft drinks are Holler or Hollundersaft. It's a soft drink made of elderberry blossoms.
Beer in Austria is largely ubiquitous with Märzen Lager. The quality is generally very good but varies greatly between breweries, as in many other Central European countries. The best options are from a modest number of remaining regional breweries not yet bought up by Heiniken. Visitors acustomed to the selection common in most larger towns in the US or UK may be underwehlemed by beer lists, even in upscale bars. There are a small number of micro-breweries around the country, offering more exotic brews such as stouts. Beer culture in Austria is not wide-spread, many Austrians have strong brand loyalty but don't know the difference between pilsner and lager, so don't be surprised if a bar tender or server struggles to answer your questions.
Schnaps is a type of fruit brandy served in many parts of Austria, usually after a meal. The most popular flavours are pear, apricot, and raspberry, though dozens of other flavours are available. There are three quality tiers of Schnaps: distilled, infused, and flavoured. The distilled variety is the highest quality; several brands of Austrian fruit Schnaps rank among the best in the world, but are accordingly expensive: a half-Liter bottle can cost up to €100. "Real" Schnaps is made from real fruit either distilled or infused. Beware of the cheap stuff sold in large bottles in supermarkets; this is often of the "flavoured" type - nothing more than pure ethanol mixed with artificial flavouring. If you want the real thing, go to a deli or upscale bar if you're in a bigger city or a Buschenschank Farmhouse if you're in the countryside. However, be careful with Schnaps especially if you are not used to alcoholic drinks!
Eiswein is a type of dessert wine produced from grapes that have been frozen while still on the vine. Eiswein is generally quite expensive due to the labour-intense and risky production process. Your best bet is to buy eiswein at Naschmarkt for €10..15 for 375 ml or 500 ml; more chances to find it there on weekends. Just to give an idea of prices elsewhere, ice wine sells at Wein & Co near Naschmarkt at €24-30 for a 375ml bottle, and Vienna duty free shop sells it for €23.50 as well.