What are the places in Vienna to visit according to a local?

Depends, of course, on what you like and who you're with. This should get you started. They are all can't miss opportunities, IMO, but not an exhaustive list. Coffee: PoC; Coffee Pirates; Caffe Coutoure; Radlager Palazzo (also to eat); van van stein; Brass Monkey; Pure Living Bakery Downtown (and for ice cream!) Eat: zweitbester; Kim Kocht; Zum Reznicek; Mochi; Big Smoke (pop up on canal -- also to drink); Moto & Moto am Fluß; Neni; Rupp (vegan Austro food); zur eisener Zeit; Cafe Dreschler for brunch; Drink / Party: Wiedenbräu in the garden; Any of the nice wine taverns (Heurigen/Buschenschank) in the hills; a million pubs; elektro göner; grelle forelle; a million clubs; Hang out: MuseumsQuartier; Brunnenmark on Saturdayt; Yppenplatz; Schleifmühlgasse area; Naschmarkt; Gumpendorferstraße; stroll Neubaugasse/Burggasse area; Sites / Sights: Wien Museum Karlsplatz; MAK; Art and Natural History museums are both great in their own ways; if you don't want to go out to the boonies, visit the Hofburg instead of Schönbrunn for your fill of palaces; Belvedere for the art and the building itself (upper guaranteed/lower depending on what's showing)

Lots of people ask me (I am Wiener), so I have written up some tips here: http://www.fasol.com/2013/08/18/tips-for-vienna/