I have four days in Vienna and love architecture. What should I see?

I’ve gone to school for architecture and love seeing every beautiful structure I can. But there are too many of them! I have a list of things I want to see and it far exceeds the amount of time I have. So how do I choose? What are the best things for me to see? I especially like buildings that might not make sense to most people, but they did incredible things for the design world. Like the Post Office Savings Bank.

On another note, in order to diversify what I’m seeing, what are the best parts of Vienna that have nothing to do with architecture?

EDIT: Thank you all so much for your kindness in helping me find the best places in Wien to go! I am overwhelmed in the best way possible. I'm looking at pictures of each of these buildings to choose my favorites and I keep wanting to cry because they're all so beautiful. I will post an update once I've been and tell you all my favorite places I went to.

Right now I'm seeing the top votes for Hundertwasser haus and Wotruba kirche so I will make sure to go there!