I would use on of the websites such as otoDom.pl ( you can enter the city and then switch to map view, to find places near where you wanna live ), unfortunately many of them are focused on students and have for instance multiple number of beds per room.
Some companies offer relocation budget - usually you can pay a proxy company to find you something of your preference.
There's a lot of this type of flats ( this one's pretty close to CS actually ):
otodom.pl/mieszkanie-wroclaw-srodmiescie-plac-grunwaldzki-id39470452.html
But it's visible from the photos it's for students.
This one's close by as well:
otodom.pl/mieszkanie-wroclaw-srodmiescie-59m2-2-pokoje-1200-pln-id39556004.html
But it's not really furnished ( beside kitchen and bathroom )
You'll have to search yourself or use an agent ( they usually take 1-2k zlotys ).
Sometimes the person who puts up these adverts is an agent, and then this means paying anyways.
Can anyone tell me how much would cost to rent a small studio in center wroclaw? thanks
I'd say 1,500 Zl per month.