Translation:No, I do not live in Tokyo.
So it's to make sure that "I do not live in Tokyo" becomes more prominent in the sentence? Instead of sort of on the side?
If you were to say, "I don't live in tokyo, but it's horrible!" (Assuming something bad happened), you wouldn't have the wa after tokyo, since it's no longer the most important?
From what I've learned so far¹, it's not about the prominence in the sentence, Insanenova. (I'd like to hear Jungerstein's reasoning, though.) One of the uses of は is contrast or opposition. So, in this case, it indicates that the person lives in another place, not in Tokyo. Think of "いいえ、とうきょうにはすんでいません" as a reponse to something like "I know you live in Tokyo. How is it?" (the interlocutor made a wrong assumption, and the answer is a correction).
If the question were simply "Do you like in Tokyo?", the answer could be "いいえ、とうきょうにすんでいません" without the は. But, in other cases, when the person is trying to say "I don't live in Tokyo. I live in another place", the best option would be to use. For example, "いいえ、とうきょうにはすんでいません。 きょうとうにすんでいます".
¹ I based my explanation from what I've read on the "Different situations, different particles" section of this: http://nihonshock.com/2010/02/particles-the-difference-between-wa-and-ga/
and watching this video (in Spanish): https://www.youtube.com/watch?v=tVBRSm74owE (you can start at 8:19)
I think the current translation is better because in English people usually use the "subject-verb-object" form, while the most common in Japanese is "object-verb". Of course you're sentence is right but you cannot always approximate sentences like that. For example, "Niku wa tabemasen" would sound more natural if you translate it as "I don't eat meat" than "Meat is not what I eat" (although the second is more similar to the Japanese structure).
In both yours and mine examples, though, we had to add a proverb (i.e. "where" and "what") in order to have a logic sentence. And that's another difference because there's no "where" in the original sentence. The meaning is the same, of course, but these are the limitations of a machine translation (even if it's man-programmed).
I'd disagree, as the sentence structure and word order are fundamentally different between English and Japanese. If we say "Tokyo is not where I live," it becomes a linking verb (is) whereas the original sentence is (I) do not live in Tokyo, which would use the "living in" verb. We can make the word order match, but it would not make the structures as analogous to each other.
This is the biggest con to duo, you only have one line to gather that context from and sometimes that context can be taken or accidently implied different ways. If there was a picture for each one liner like this, the imply wouldn't be needed. What I have been doing is paying close attention to the words and forming a scenario or action with my hands (like pointing) to help the context be more clearer/revealing.