What are some must-sees in Vienna? I'll be there for two

Visit Mozart's apartment. It's been turned into a museum.

>modern art
In that case I could recommend especially the MUMOK (Museum of Modern Art) or Leopold Museum right opposite of it. They're both inside the Museumsquartier, along with some restaurants that have relatively cheap meals from about noon to 3 pm (mqdaily.at is really good)
Other than that, the Albertina Museum behind the State Opera has a great collection that covers mostly 20th century art.
Belvedere covers everything from the Middleages to now, so there's plenty of great modern art. It's not exactly inside the city centre, but alone the castle & surrounding park are worth the trip.
If you're on a budget or have little time, try the Kunstforum or go to MAK (Design Museum) on Thursday evening, the entry's free from 6-10 pm

>modern architecture
How modern? If you're into Art nouveau, check out Otto Wagner's Postsparkasse and the Pavillion on Karlsplatz. Otherwise the Loos-Haus on Michaelerplatz is a must-see. The Loos American Bar (in a side alley of Kärntner Straße) isn't that crowded with tourists, on the other hand.

Thanks, that helps. I had a lot of those on my list anyway.

I'm not sure about castles like Belvedere or Schönbrunn because as I said before, I'm German and have seen quite a few castles in Germany and other parts of Europe, so I feel it might not be as interesting as for someone from outside of Europe. Then the castles in Vienne are not really inside the centre and I have only about two days, so I'm sure if they're worth my time.

>>1202528
Hunderwasserhaus and incineration plant Spittelau (also designed by Hundertwasser) are really nice

Kaisergruft

Must see.

>>1202259
The DC tower looks quite interesting.

>>1202581
Yes, the incineration plant is nice...odd to say that, but it's Vienna; there are a lot of nice things to see.

>>1202528
Go to Schönbrunn! I too have been to many other castles in Europe; this one is the best IMO. It is a must see!

>>1202259
You need to visit the KHM, Neue Burg, Schatzkammer, Theatermuseum and the Wagenburg.

https://www.khm.at/
http://www.kaiserliche-schatzkammer.at/
http://www.theatermuseum.at/
http://www.kaiserliche-wagenburg.at/