"What kinds of cities do you know?"
Translation:Milyen városokat ismersz?
I think our English experts may say that "what kinds" is kind of wrong, and it should be "what kind". Not sure. (Please correct me if I am wrong.) So I am not sure what is the difference, or if there is a difference, in English.
Anyway, I can't think of any difference in Hungarian. The noun is plural (cities - városokat), and the question word "Milyen" must stay singular. It works like an adjective before a noun.
I would say that both are possible; what kind of cities is more about one group of cities with a particular characteristic (e.g. "big ones") while what kinds of cities implies that you know multiple groups of cities, each with its own characteristic (e.g. "rich ones, poor ones, and in-between ones").
In that case, we can introduce a new word: "fajta". Some of you already know this word. In this context, it means "kind" or "type".
So, you could say:
"Milyen (fajta) városokat ismersz?" - This could be about one group, but not necessarily.
"Milyen városfajtákat ismersz?" - This is the case of the multiple groups.