Third Person Plural Pronoun for Inanimate Objects in Accusative Case

Question

I know that for animate objects the third person plural pronoun is их:

— Ты знаешь Мишу и Катю?

— Нет, я их не знаю. ( Нет, я этих людей не знаю. )

However, I am not sure if we use the same pronoun when talking about inanimate objects:

— Ты знаешь Лондон и Нью-Йорк?

— Нет, я их(?) не знаю. ( Нет, я этих городов не знаю. )

Do we use the same pronoun in both cases?

Answer 1

Yes, они has the accusative их for both animate and inanimate. (Your intuition is correct about there being a "missing" inanimate form; it was supplanted by the animate one and went extinct. Had it survived, it would've been е or, confusingly, я.)

Answer 2

Both are possible, though the second pair is wrong.

"Ты знаешь Лондон?" means "How well do you know the city of London?", so the right answer would be, for example, "Совсем не знаю".

Also consider that spoken habit of omitting pronouns:

Q: Ты знаешь Мишу и Катю?
A: Нет, не знаю.

Answer 3

Yes, it is usually OK to speak of cities, etc. using "их". But in case of answering a question it depends on the form of that question. In your second example, the question doesn't include the word "города" (e.g. "такие города как"), to which "их" in the answer would refer. So an extended answer (as opposed to "нет, не знаю") to that question should use something like "этих городов" as you wrote in brackets, rather than "их". However, in case there IS "города" in the question, you can surely use "их" in the answer:

 — Ты знаешь города Лондон и Нью-Йорк?    — Нет, я их не знаю.

("их" refers to "города", not to city names)

— Ты знаешь такие города как Лондон и Нью-Йорк?
— Нет, таких не знаю. (— Нет, я их не знаю.)

— Ты знаешь Лондон и Нью-Йорк? — Нет, этих городов я не знаю. (The short form: Нет, не знаю.)

So, generally you need some additional context to perfectly use "их" when speaking of city names: that pronoun typically replaces 'cities', not their names.