My advice is to get out of the first district for authenticity. Vienna is a surprisingly small and compact capital with excellent public transportation, so moving out of the first is easy.
I would suggest that you explore neighborhoods such as the area around Yppenplatz and Brunnenmarkt:
http://www.wien.info/en/shopping-wining-dining/markets/yppenplatz-restaurants
...the area around the Karmelitermarkt:
http://www.wien.info/en/shopping-wining-dining/markets/karmeliter-district
...walk down Neubaugasse/Lindengasse and head over to the Spittelberg area
...enter the MuseumsQuartier complex and check out the scene there
...or wander the south end of Langegasse.
In all of these areas you will find interesting and local eating experiences.