Which cities were the main centers of industry and culture in the 1890s?

"Industry" refers to making things, especially using machinery in factories. It can also refer to specific businesses, even when they are not actually making things. IOW the word has no strict definition.

"Culture" is derived from an ancient word for a plow. Related words are cult, cultivate, colon and colony.

Bottom line: every city was a main center of industry and culture.