It's actually a disgrace how hard it is to find an internet acces here. But this tip might help you: there is a free one in a student place called K4 on Kersnikova 4. It is where the bus stop Bavarski dvor is, you just have to go around those buildings and get to Kersnikova street. You will see it when you are there.
For using internet upstairs you will probably have to order coffee or something, but dowstarirs is free.
There is also Internet at the train station.