Putting this here for future reference. Part of a series - see this.

Without further ado:

Zum Weissen Rauchfangkehrer
Pricy, Austrian, very good food
Weihburggasse 4, 1010

Pure Living Bakery
Great US-style coffee place
Burggasse 68, 1070

Die Burgermacher
Best burgers in Vienna
Burggasse 12 1070

Glacis Beisl
Breite Gasse 4, 1070
Good Austrian food, reasonable prices

Benkei
Very good sushi
Ungargasse 6, 1030

Suessi
Cute French tea salon
Operngasse 30, 1040

Cha No Ma
Japanese tea
Faulmangasse 7, 1040

Sebastiano
One of the best Italian restaurants in Vienna, reasonable prices
Mayerhofgasse 22, 1040

Indien Village
One of the best Indian restaurants in Vienna, reasonable prices
Hohenstaufengasse 7, 1010

Taste of India
Good Indian food
Margaretenstrasse 34, 1040

Daniel Moser
A Viennese cafe with decent coffee (rare)
Rotenturmstrasse 14, 1010

Griensteidl
A traditional Viennese cafe with nice food
Michaelerplatz 2, 1010

Kaffeefabrik
Tiny hole in the wall place with maybe the best coffee in Vienna
Favoritenstrasse 4, 1040

Dino's American Bar
Best cocktail bar in Vienna
Salzgries 19, 1010

Barfly's
Very good cocktail bar
Esterhazygasse 33 (in the Fuerst Metternich Hotel)

Update (September 2016): As I write this, I haven't lived in Vienna for 3 years. I go back about once a year. To the best of my knowledge, all places above are still open and haven't changed.

Sapa
Laid back Vietnamese restaurant with good French pastries for dessert.
Lindengasse 35, 1070

Kaffemik
Another very good third wave café in Vienna.
Zollergasse 5, 1070

Kaffeeküche
Best croissants in Vienna - better than those in Lyon! Good coffee.
Downstairs in the Schottentor metro station, 1010