Visit Brno
You will find information about what to do in Brno here
https://www.ticbrno.cz/en/uvod
We recommend taking a walk through the park to the castle of Spilberk (Špilberk) as there is a wonderfull view of Brno there.
https://www.spilberk.cz/?lang=en
You can visit some of the historical underground facilities in Brno, you will find more information on:
https://www.ticbrno.cz/en/podzemi/kostnice-u-sv-jakuba
Or the famous Villa Tugendhat - though I recommend to book tickets in advance if you are interested in seeing it because all the tickets are often sold out.
https://www.tugendhat.eu/en/homepage.html
Restaurants:
If you would like to try the Czech cuisine, you can go for example to:
restaurant Na Švábce: https://www.nasvabce.cz/index.php/en
the bistro U Dobrého pastýře: https://www.udobrehopastyre.cz/ (but the opening hours are only from 11 to 15 on weekdays)
If you prefer veg(etari)an food, you can eat well in:
Kupé: https://www.kupeorient.cz/
Vegalité: https://www.vegalite.cz/
But there are many more restaurants with good food and good beer or wine, it is up to you. :)