This is the 1455th most frequent Polish word.
łódzkiego
"Łódzkiego" means "of Łódź" or "related to Łódź," referring to the Łódź region in Poland.
The word 'łódzkiego' here is the masculine singular genitive form of 'łódzki,' modifying 'województwo'.
Mieszkam w województwie łódzkim.
I live in the Łódź Province.
In this sentence, 'łódzkiego' is the masculine singular genitive form of 'łódzki,' used to describe 'miasta.'
Odwiedziłem stare zabytki łódzkiego miasta.
I visited the old monuments of the Łódź city.
Here, 'łódzkiego' is used as a genitive modifier of 'regionu,' indicating possession referring to Łódź.