Brno is small enough that the ring road is the only boundary that matters; everything else is a trade between tram noise and a ten-minute walk.
Brno-stred - inside the ring
The core between Zelny trh, namesti Svobody and Petrov hill. Every sight, bar and tram line is a walk from here, which is exactly why it is the most expensive square kilometre in the city.
Veveri and Udolni - the university side
West of the ring, where the Masaryk University faculties and the student pubs are. Rooms are cheaper and the centre is a five to fifteen minute walk, but the streets go quiet in July and August when term ends.
Around the main station
Scruffy, busy and where the cheapest beds are. Every tram line passes through Brno hlavni nadrazi and the old town starts about ten minutes uphill, which makes it the sensible choice for a late arrival or an early train.
Stare Brno and Mendlovo namesti
Below Spilberk beside the Starobrno brewery, roughly fifteen minutes on foot from the centre and on the tram line out towards Pisarky and the exhibition grounds. Quieter and cheaper than inside the ring without being out of reach of it.