Although Brno has its own airport called Brno-Tuřany, with regular Ryanair flights to London, Berlin and Milan, most visitors to the city fly to Prague or Vienna and travel the rest of the way by bus or train.
You can reach Brno from Vienna International Airport by bus or by train. Each option costs appx. 15 EUR each way (if bought in advance).
From the Main Station (which is the main hub in Brno located next to trains and buses) you can continue 6 minutes by tram No. 1 in the direction of Bystrc-Ečerova and get off at Mendlovo náměstí (Mendel Square). From there you can either walk or continue one stop by bus No. 84 to Křížkovského stop.