what about Vienna ??
There is an EC-Train (EC71) departing at 07:43, arr.VIE South-Station at 9:28,
then take the "D"-tram, 4 stops only ,to the famous Vienna-Ringstrasse, 5 minutes from the Opera-House and City-Center
return also by EC (EC 70)at 18:33, arr. Brno at 20:21
Why not give it a try ?
Not really a must see, but an essential I guess.
In my experience trains in Czech run pretty much to time, but aren't the fastest way between two points.
I used the train several times a week to get in from Zastavka to Brno on evenings out and to go to the bigger shops and the market.
The station also has a post office right next door that is open 24 hours a day and on weekends when others are closed.
In 1839 The city of Brno got its link to Vienna via the Northern Line. It was the first city in the Czech countries to get this link. Todays station building dates from 1850, while during 1902 - 1905 it went through a reconstruction