what kind (no s) should be accepted. reported. wouldn't kindS be milyenek? not sure.
Both should certainly be accepted.
I think the sentence translates more literally as "What are the cities that you love like" or "What are the cities like, that you love?" (For clarity, I've translated "szeret" as "love" in both of those.)
Now, "What kind of cities do you like" asks more for a single explanation for what cities you like. "What kinds of cities do you like" suggests that there might be multiple explanations, or multiple types of cities that you like.
If I understand right, the Hungarian sentence doesn't so much favor either.
In itself, maybe. But since it is in front of a noun, the same rules apply as with adjectives. It stays singular in front of a noun, and turns plural after a plural noun.
"Milyen városokat..." vs. "azok a városok milyenek?".
This "kinds" of question comes up all the time in Duolingo sometimes they accept 'kind' other times it's "kind/s" and occasionally both are accepted I just wish we could have some consistency. I do report it each "time/s" btw.
Must the "kind" be included here? Or could one say "What cities do you like?"
I think that would also be an acceptable way of saying that. You should report it as a suggestion.