all the places on the list are good. My favorite is the 1st district or city centre. Spend some time in various parks located throughout vienna, this time of year they are beautiful. Also, locals love to go to a “Heuriger”. There you can enjoy wine and relax and possibly watch an austrian dance and play an accordian. Im not sure if they all do, but many have green lights in front of their small buildings, so thats how you can tell if its a Heuriger. Millenium City is a cool shopping center. There is so many really cool night life places along the danube canal, and also many cool bars on the Gurtel. The Danube Tower is expensive, but amazing to have dinner in. It rotates around so you can get a panoramic view of Vienna. I could go on and on but I dont think you’ll have enough time to visit all these places anyway. I hope you enjoy your trip!

Adding to what Freest said about heuriger, you can tell it’s open if it has a little bit of pine branch hanging outside it.
Food drink items, ice cream in Schwedenplatz, and the hot dogs at the dodgy looking kiosks in the city center are also really good – and not as dodgy as they look!! There are also a lot of little shed things where people are cooking and selling hot potato wedges and chestnuts, they’re yummy.
I would recommend trying erdaepfel salat (potato salad). It’s different to what you might be used to. Maybe not strictly viennese but it’s good!
If you go during Vienna’s winter, don’t miss the Christmas markets. And if you go to the Christmas Markets, go get a nice hot cup of berry punch! (and keep the mug).
I could go on forever… there are a million and one fantastic things in Vienna.
Have fun!