Visited January this year. Hope you get better than our zero centigrade.
There are plenty of the traditional cafes around the Innere Stadt area and most have seem to have maintained their authenticity despite the potential to be a tourist trap. One stand-out for us was the Cafe Central at Herrengasse 14
There are numerous Aida cafes around Vienna but one with a very nice vibe that we found was Prousek & Co. Chocolaterie & Grosskonditorei at Wollzeile 28 1010 just down behind St Stephans at Stephansplatz.
Hope this helps. Enjoy your stay.