There's nothing wrong with in Tokyo in Koganey , except that it might be confusing, particularly if people are not familiar with the place names and their relationship.
I would say either I live in Tokyo, in Koganey where the comma indicates that the last phrase is an afterthought, making the sentence more precise; or I live in Koganey in Tokyo where it does not make any difference to the meaning whether it is parsed as [in Koganey in Tokyo] or [in [Koganey in Tokyo]].
Even clearer is
I live in Tokyo, in the Koganey district.
or I live in the Koganey district of Tokyo.
ell.stackexchange.com/users/1780/Colin Fine
There is no rule that dictates which preposition follows another.
In the case of "nested" prepositional phrases, use the word that best fits the context .
That's the easy part of the answer.
The hard part is helping you understand when to use "in" vs. "at".
These little prepositions typically have around one or two dozen different meanings and usages, some of them overlapping, making them notoriously easy to spell but difficult for learners to use.
(For example, this site recently had a lot to say about in the park vs. at the park – neither of those is "incorrect;" they say sort of the same thing in two different ways.)
In the context of describing a physical location, the word in means, roughly, inside the confines of .
Generally speaking, in the building means inside the building , while in the city means within the city limits .
In the context of describing a physical location, the word at means at the location of .
Think of it as a point on a map.
Your examples gives a location within a location.
When talking about a neighborhood, suburb, or district, in most cases, I would use in both times, perhaps separated with a comma:
I am living in Tokyo, in Koganey.
He is staying in Sydney, in Camden.
She is working in New York, in Manhattan.
However, when talking about a hotel or other building, I would use at instead of in : I am living in Tokyo at my friend's house.
He is staying at the Four Seasons hotel in Sydney.
She is working in New York at an upscale restaurant on 44th Avenue.
ell.stackexchange.com/users/113/J.R.
If I have understood your question correctly, the confusion is between in and at while describing city as a living place.
True, I'd use in to mention 'living' in open spaces such as cities here.
But then, I have observed (though rarest cases) that the preposition in is used to mention larger cities .
And, for small places like towns, villages and small cities, using at is also evident.
But anyway, standard practice is to use 'in' and not 'at' because when you use 'at', you describe some 'point' and city, by large, is an open space.
Koganey is a small city in Tokyo and Camden is a small town in Sydney. .
at is proper to mention some place in a city.
Good read here (note in New York ).
The BBC on prepositions , clarifying all doubts here.
And yes, do mark Colin's suggestion of putting two commas to have a better construction.
ell.stackexchange.com/users/3187/Maulik V
I am staying in Tokyo at Koganey.
He is staying in Sydney at Cameden
Usually, when we refer to two locations/places in a sentence one after the other, we use the preposition "in" before the main/larger location and "at before the location which is smaller or shows a point in the main location.
So the use of the "at" and "in" in the above sentences is correct.
However, it's also correct if you use the preposition "in" before both locations but you should put a comma after the location mentioned first.
ell.stackexchange.com/users/9259/Khan
in and at are used for similar things in regards location.
Sometimes they can be more or less freely interchanged, but other times one is used more typically than the other.
For example, you generally use in with cities, states/provinces, countries (regions) I live in London
He used to live in California
She spent a summer living in France
None of these would typically have at in them.
at is used for general locations
He is at home
She is at work
It is also used for buildings and other smaller locations (points)
He is at the movie theatre
She is at the Empire State Building
It is more ambiguous or at least either could work in between these two extremes.
Regions within a city or country could be in or at, partially dependent on whether they are thought of more like a point or a region.
He is staying in Sydney at Camden in comparison to
He is staying in Sydney in Camden
The first sounds more natural to me, but it also treats Camden more as a single point.
The second one implies Camden is a region; however, it also seems to imply Sydney is part of Camden (rather than the reverse).
This nesting doesn't happen with at ; It would be more natural to express the second sentence as He is staying in Camden, Syndey at doesn't have this nesting effect.
That is, He is staying in Sydney at Camden does not sound like Syndey is a part of Camden.
This would be because at is like a point and thus can't really contain another region.
ell.stackexchange.com/users/12503/eques
I am new to English language. I have seen many times when the word "in" is used to explain an area "at" is also used following it.  For example:   I am living in Tokyo at Koganey.   He is staying in Sydney at Camden.   I want to know that why it can not be written as:    I am living in Tokyo in Koganey.   Is there a rule to follow when writing like this?  I would be grateful if you could give a clear explanation about this.
is it a rule to put "at" after "in"?
ell.stackexchange.com
<prepositions><collocations>
ell.stackexchange.com/questions/43263
ell.stackexchange.com/users/13814/tnishada
There is no rule that dictates which preposition follows another. In  and  at  are used for similar things with regards to location. Usually, when we refer to two locations/places in a sentence one after the other, we use the preposition "in" before the main/larger location and "at" before the location, which is smaller or shows a point in the main location. There's nothing wrong with  in Tokyo in Koganey , except that it might be confusing  if people are not familiar with the place name. There are no set rules, you can use either.
There are no set rules, you can use either.