Pretty easy to find veggie or veggie-friendly restaurants in Vienna:
https://www.tripadvisor.com/Restaura...40-Vienna.html

Most tourism focuses on the historic inner city - the 1010 zip code - with traditional / touristy restaurants (which does not necessarily equal 'bad') while other parts of town are much more "contemporary" like Spittelberg, Southern part of Neubau district - from Museumsquartier (MQ) almost to Westbahnhof (very roughly).

Please don't call the medical association on me, but a lot of Viennese cakes and pastries are filled with nutrients. Even Sacher Torte -- which I find irresitably wonderful, every time -- is made of ground nuts. Apple strudel and other cakes and pastries made with cheese, eggs, fruit, nuts (including chestnuts) and seeds. In 3 days, if you don't have food issues prohibiting suga, etc, you are unlikely to do yourself much harm eating as many Viennese cakes as you can manage.