Are "我在哪里可以买火车票" and "我哪里可以买火车票" both correct sentences? If one isn't, why?
The proper way of asking is "我在哪里可以买到火车票?". Most Chinese would be able to understand your question even if you were to use the two sentences you have just written.
I saw many comments asking about the correctness of different variations to the question. Although not directly relevant to the question itself, here are some of the variations:
我在哪里可以买得到火车票? (Where can I buy (a) train ticket?)
我在哪里可以买到火车票? (Same as above, less emphasis on getting the ticket)
哪里可以买得到火车票? (Where can train ticket(s) be bought?)
哪里可以买到火车票? (Same as above, less emphasis on getting the ticket)
哪可买到火车票? (Where can buy train ticket?)
哪有卖火车票? (Where got sell train ticket?)
去哪买火车票? (Go where to buy train ticket?)
If you are asking a stranger for directions, it would be prudent to ask in this manner:
请问哪里可以买得到火车票? (Excuse me, where can train ticket(s) be bought?)
"我在哪里可以买到火车票?" is the correct way to ask where you can buy the ticket, but in oral language "我哪里可以买到火车票?" is used quite often.
Actually there are 2 ways how "我哪里可以买到火车票" can be interpreted. The first one is a question asking where you can buy train tickets. The second one is a statement meaning there is no place where train tickets can be bought. In oral language people will know what you mean by the context, the tone of your voice and your expressions.
Sometimes 我哪里可以买火车票 without a questioning tone means can be used to indicate someone who can't buy a train ticket for some obvious reason (both talker and listener understanding the situation). Similar to the rhetorical "Why can't I buy a train ticket?" in English.
This case occurs in some disputation, and 我哪里 is emphasized.
there is a case: A: 你从火车站回来怎么不买火车票呢，明天买票排队要花很长时间呢。 B: 我哪里可以买火车票啊，昨天不是把钱都给你了嘛，我现在身无分文。 A: 哦，我忘记了。
In oral Chinese, we can understand you, but in writing Chinese, only one statement without tone, there may be misunderstanding.
1.我哪里面有时间陪你看电影啊，我今晚要加班。(I can't go to the cinema with you because I must go overtime work this night)
“哪里” sometimes means “how can I do this” or “It's too difficult for me”.
我在哪里可以买到火车票 = Where can I buy a train ticket? 我哪里可以买到火车票 = Why do you think I could buy train ticket?
When 哪里 follows 在、去、到 it means somewhere.
When 哪里 follows someone or something it may mean “how can I do this” or “It's too difficult for me”.
他哪里能完成这个项目 = He cannot finish it
你哪里能承担责任 = You cannot be responsible for this thing
BerR's answer is correct. I have a supplement of the second expan of "我哪里可以买到火车票". It is not only a statement that there is no place where the tickets can be bought, but no ways, no time or the tickets are sold out objectively like and so on, any situations that you can not buy the tickets, you can say that sentence with falling tone.
BertR's answser is right. But it depends on the circumstance you can saying it, if you are in front of the train station, you ask someone "我哪里可以买到火车票" instead of "我在哪里可以买到火车票?", one can unterstand you want to buy ticket, they are almost the same though it seems not correct to say "我哪里可以买到火车票" to some extent. But when your friend ask you to visit him, and you are failed to buy a ticket, you can say "我哪里可以买到火车票", it means the ticket is difficult to buy, this saying is a kind of complaint.