This is the 16033rd most frequent Polish word.
tutejsze
"Tutejsze" means "local" or "from here."
Here, 'tutejszego' as a form of 'tutejsze' applies to the noun 'miasta' (city) and indicates it is the local city.
Mieszkańcy tutejszego miasta są bardzo uprzejmi.
The residents of this city are very kind.
The word 'tutejsze' refers to the adjective 'local' in the context of describing forests in the nearby area.
Tutejsze lasy są bardzo malownicze.
The local forests are very picturesque.
In this sentence, 'tutejszej' modifies the noun 'obsługi' (service), signaling it pertains to the local establishment referred.