How to survive a day like this? I prefer sunny day instead of raining. But when you must wake up, there is no chance to be alive without coffee. If your apartment is not equipped with a coffee machine like mine, you will presumably buy a cup of coffee out. Some of us have to go to work/school... whatever. You will probably fight inside you to not fall asleep because the consequences might be dramatic. E.g. I cannot affort that such situation will take place therefore I could lose my job.
Do you want to know how I deal with boring day, but not drinking coffee at all? In my veins flow energy drink, I assume, because I sleep not much. Excercises allow to feel better for the rest of the day. In Krakow you will find plenty of gyms. Sometimes, when you don't have to much time to go to the gym, you can also do jogging 3-4 times a week before your breakfast. Then you can rule the world! :)
In case of a leak in your plan, you can always go with someone else to the cinema (Multikino, Cinema City) and watch film you interested in or go to the theatre (Bagatela or Słowackiego). Many academic circles in Krakow organised events involving meetings with famous people like actors, singers, journalists, CEOs and so on. Most of them are opened and you can join and hear what that person (or a group) wants to say. Probably after the event you may take a photo of you and celebrity/star.