Does 「你的中文是在哪里学的？」mean "How did you study Chinese?" or "Where did you study Chinese?"

哪里=where. Period.

Suggestion out of topic:

When someone told you "你的中文太好了", you answered:

谢谢

My suggestion is to answer "哪里哪里" (not so out of topic, after all :-)

Edit:

请看看以下视频:
1。中国人自谦爱说“哪里哪里”，外国人就没法理解了
2。请注意他说："轮到一个中国人说'你讲得很好'，我一定说'哪里哪里'。'你讲得很好'，'谢谢你的夸奖'，他嘴巴不讲，心里就开始反感了"

Strictly speaking, what he asked is where.

But in daily oral communication, as a native Chinese speaker, I can tell you both where and how is ok to answer.

I mean

If one person asks you 你的中文是在哪里学的？（where） and you answer "My friends taught me"(how)

Or

If one person asks you 你的中文是怎么学的？（how） and you answer "In 北京语言大学"(where)

Every Chinese can understand you and even sometimes we ask like this.

Because broadly speaking, this sentence is to ask you in what ways, by what means, through what, where, how you learnt Chinese. It's not in a narrow sense where and how. You should figure out what he wanted to express instead of literal meaning.

I agree with @dan's answer. Just like that "China always win" joke, the interpretation of this "question" depends heavily on the context.

Specifically, this rhetorical expression is mostly used colloquially where additional context can be provided via facial expressions, stresses and the general tone of the sentence.

I think there might have also been a tone particle like 啊 or 呀 you missed which would have made it clear it was rhetorical/exclamational. I.e. "今天天怎么这么冷?" could be a question or an exclamation, but "今天天怎么这么冷啊!" is undoubtedly rhetorical.

他问的是 how 你回答的是 where.

This explanation is poorly done. I think what your friend was trying to say was "他问的是 how [come your English is so good] 你回答的是 where".

This involves another phenomenon where Chinese people read between the lines and respond to the subtext.

Also, as the listener may not be 100% sure if the expression is being used in a commendatory or derogatory sense, this kind of response strategically indicates which way the listener understood it as, which gives the asker a chance to clarify.

For example, this is a perfectly normal Chinese conversation:

A: 你这鸭脖是在哪里买的啊! (Read "This duck neck tastes so good!")
B: 楼底下超市*，好吃我明天再买

* In this case, answering the question literally is okay as the asker may actually be interested in that information.

And a derogatory version:

A: 你这车是哪里学的?! (Read "Your driving sucks!")
B: 我下次会注意

In this case, it is unlikely that the person is interested in the name of your driving school.

Your friend skipped a step and didn't explain this thinking process.

When a Chinese person ask you: 你的中文是在哪里学的？ He actually want to know: which university, province or city you learned Chinese at?

And another implied meaning is that: Your Chinese is very good, so he is very curious and ask you this question.

When a Chinese person says 你的中文是在哪里学的? usually means you speak Chinese very well and just make him wonder why you learn so well! He may not care where you study from

The question 你的中文是在哪里学的 is not quite correct.

I think the correct question should be: 在外国人里,你的中文真好,是怎么学的?

中国人：你的中文是在哪里学的？

我：在北京语言大学学的。

Without other context, this dialogue indicates a normal conversation sequence. '在哪里' just means 'where'.

In some context, 你的中文是在哪里学的？ could be used as a rhetorical question. The underlying meaning is 你的中文是在哪里学的？ (怎么这么差！) In English, it could be something like from where have you learned such awful Chinese? In this case, they may not want you to answer it literally. And I guess you don't want to answer it at all.

Out of that specific context, 你的中文是在哪里学的？ is just a normal sentence and your answer is a proper one.

To me, 在哪里(where) doesn't mean 怎么(how) in any case. And your Chinese friend might say it out of certain context, in which you should use 怎么 other than 在哪里，otherwise he is plain wrong.

Edit:

Context is the key here. 你的中文是在哪里学的？could also imply someone's Chinese is very good and they want to know where they have learnt it. But standing alone, we can't make any assumption about the context. We should take it literally instead, unless OP can provide more context for analysis.

Edit:

中国人：你的中文是[在哪里]学的？ indicates the question is asking 'where'

中国人：你的中文是[怎么]学的？ indicates the question is asking 'how'

中国人：你的中文是[从哪里]学的？ indicates the question is asking 'from what source' And sources are not locations -- For example: from books, from classes, from T.V.

'From what source' = 'with what methods' --> 'how' you learn

When the Chinese person asked '在哪里学的' but then claimed he was asking "how" he should have said 从哪里 instead of 在哪里

'在哪里' refers to 'what location' e.g. Hong Kong, Beijing, Shanghai.

'从哪里' refers to 'source' e.g. books, classes, the internet.

Does 「你的中文是在哪里学的？」mean “How did you study Chinese?” or “Where did you study Chinese?”

It means “Where did you study Chinese?"

I think the trick here is that 学 doesn't necessarily stand for 学习 (study), it stands for 学会 (learn).

Thus they are asking: "Where did you learn Mandarin?".

Unlike "studying", "learning" a language can be a passive process, and can come from a variety of sources. Maybe you speak it at home with your parents, picked it up while working in China, etc. Having studied it is one of the options.

So 在哪里 assumes a broader, figurative meaning in this case. You can also see this as: "How come you can speak Mandarin?"

If you see it this way, your original answer isn't very spot-on in English either.

Since you are not required to point out a specific place, valid answers might be:

我父母是中国人, 我男/女朋友是中国人, 我在大学念中文, 我在中国工作了5年了, 我每个周末跟我的中国朋友一起去打台球, etc.

To reduce ambiguity and ask in what place someone studied Chinese, you can say:

你的中文是在什么地方学的？