Translation:No, I do not live in Kyoto.
In this context (as in there is no context) I don't think it matters. You could use both には or に. However, the meanings are slightly different. に marks the topic while は is more of a subject marker. As an example, using only に would make the sentence more literally mean "I do not live in Kyoto" while using には makes the sentence translate to more "As for Kyoto, I don't live there." Depending on the situation, you would use one or the other. Someone, please correct me if I'm wrong.
I think the first part of the comment was wrong: に here marks the location, and は is the one to mark the topic. Actually, I think は always sets the topic of the sentence (topic as "what you are talking about"). In this case, は's function is to stress that Kyoto is not where you live.
Your examples were right, though. As は marks the topic, it is like you are saying "as for ....,"
You could say that too, but the nuance would be slightly different.
What you wrote simply means that you live in Kyoto, while the sentence with the subject marker "wa" as in "Kyoto ni wa..." has more emphasis on (not) living in Kyoto.
What I mean is, if you use "... ni wa" in a sentence then you are implying that while you don't live in that place, you live somewhere else.
I hope this wasn't too complicated.
I generally prefer memorizing whether to use で or に for each verb because it is sometimes difficult to distinguish between the two.
However, in grammar, で is to represent the place where an action takes place, whereas に is to represent the place where the subject stays after the action takes place. In this case if you live in a place, you stay in the place, so it uses に.
this question was broken when presented in the form of an audio sample and word bank. There were several ways to spell out this exact answer but it marked all of them wrong. I even turned on IME and typed it out but it still marked it wrong, it would only accept the answer after I selected a very specific arrangement. Which took a lot of wrong answers to find.
Please report via the report flag or this page: https://support.duolingo.com/hc/en-us/articles/204728264-How-do-I-report-a-bug-
Anyone have a good explanation why arimasen isn't used? I've seen some other questions referring to livinf things with arimasen being used but then i see imasen being used for others referring to living things. I cant even find a good google reference for this besides "just use arimasen for all references living or negative" yes ive read that twice now from two different sites :-/
いる and ある become auxiliary after attaching to て and lose their original meaning. In English, verbs like "do," "can" are auxiliary verbs. Originally it is "I do work" or "It is a can," but when they are auxiliary, "I do not eat" or "I can eat," and their original meanings are lost.
There are mainly two meanings of ている. One is to represent a continuous action, the other is to represent a continuous state. 食べています means eating (continuous action). 結婚（けっこん）しています means married (continuous state).