This is the 17186th most frequent Russian word.
столичной
"Столичной" means "of the capital" or "capital-city-related."
Here, 'столичной' is an adjective modifying 'части' (part), describing it as related to the central/capital aspect of the city.
Я часто гуляю в столичной части города.
I often walk in the central part of the city.
In this example, 'столичной' relates to 'жизни' (life), indicating the metropolitan or urban lifestyle characteristic of a capital city.
Многие обожают вкус столичной жизни.
Many adore the taste of city life.
Here, 'столичной' modifies 'газете' (newspaper), signifying that the newspaper is associated both content-wise and contextually with the capital or central region.