The Cafe Sperl (open 07:00-23:00 M-Sa; 11:00-20:00 Su; Jul/Aug: closed Sundays), just minutes away from the Babelsbergerstrasse stop on the U-2 metro line and behind the Technical University, is a Viennese landmark going back to 1880 when it was first built. It's been a listed building since 1980 and has been painstakingly remodeled according to original plans. It is the closest thing you'll probably ever see to the way cafes were during their heyday during the days of Kaiser Franz Josef.
It's no longer the hang-out of military officers from noble families, but there are plenty of artists, writers, and academics of various sorts who frequent it. Indeed, they frequently stage poetry readings, play readings, and other events of some little cultural importance here.
As for things to eat, the menu is pretty broad, though thoroughly Austrian. The pastries are first rate -- try the Apfelstrudel -- and the Wienerschitzels are as good as you'll find anywhere. As for the coffee, it goes without saying, in this city of coffee fanatics, that it is tip-top.
Coffee House Cultural Notes:
It's a generally accepted thing that you are entitled to stay as long as you like while sitting over a coffee -- even the cheapest and tiniest espresso. You will never be urged to leave.
Sharing Tables
If a person is sitting alone, it is permissible to ask permission to sit down. That doesn't necessarily mean that any conversation will ensue. However, it does mean that if you walk in and find no empty tables, you can still be served if there is an empty chair somewhere.
Newspapers & Magazines
One of the great things about cafes is that you can check out the newspaper/magazine racks, choose one, and catch up on the news. At the Cafe Sperl, they provide the International Herald Tribune, the Financial Times, and The Economist for English speakers. If you read French, you'll find Le Monde and Le Figaro, too.