I also live in Katowice, so if I can add something:
There's actually alot things to see in Katowice:
- Nikiszowiec - it's a very beautiful part of Katowice, most of the district is covered in red-bricked buildings, but this place is for sure prettier in summer ¯_(ツ)_/¯
- Silesian museum - this museum is actually nearby Spodek so you can take a walk or bus/tram to visit it.
- Jumpcity Katowice - if you want to have some fun in slightly different ways than drinking or dancing, jumping around on trampolines should be just fine
- Mariacka street - a looooot of pubs where you can drink as many alcohol as you wish, eat some decent food and meet (or something more) some bishes
Also about travelling - the cheapest way is obviously by feet, but public transport can take you anywhere and tickets costs 2,40-4,80zł (1 city - 3 nearby cities). In places where buses can't take you, trams will (and the other way around). If you don't want to use public transport, Lider Taxi or Uber are the cheapest one.