Krzysztof:
You've got the "a" and "o" wrong, you probably meant Bielsko-Biała, didn't you?
It's a city with a little below 200,000 population, I have never been there, so I don't have any first hand information (except for the volleyball team, which I often see on TV).
It's located in the Beskidy mountains, so it's a great place for people who like nature, hiking, alpine and cross country skiing etc.
There's an aero club too (with sections: planes, gliders, parachuting), several indoor pools, some tennis courts and an open air ice rink.
If you like female volleyball, they have a very good club there.
taht is for me I like nature
There's a multiplex cinema there.
Centro Italiano di Cultura (thanks to a Fiat factory, so probably there is an Italian community in Bielsko-Biała).
If you're a religious person, there are Catholic and Protestant churches, (and according to Wikipedia a Jewish kehillah, some Buddist centers, Jehovah Witnesses).
If you mean night life, then I really don't know.