Bar Mrtvá Ryba, in translation “death fish”, a non-smoking bar with long history, is a purely student’s lair where you can always find young people (i.e. from the Natural science or Medical faculty) usually waiting for their next lecture or just chilling out after one. I remember I spent a lot of time there waiting for lectures and I honestly have to say I missed my lectures once or twice. If you see a bunch of people in suits there, they are for sure students who just passed some exam.
I like to sit outside under the trees belonging to the Botanical garden, which you can enter for free through the entrance close by. Aside from great beers (my favorite is Černá hora 11°, but also Klášter, Zemské pivo or Merlin are a good choice) I can recommend various wines which are worth trying.
During lunchtime I especially recommend you try the Chilli con carne, which is my favorite.