I translated this as "Where are we going with the train?" I think this makes sense in some contexts.
Two bandits rob a train and take control of the engine room. One says to the other, "Where are we going with the train?"
Two children playing with toy trains. Child #1 carries one off with an unknown purpose. Child #2 asks, "Where are we going with the train?"
"Where are we going by train?" sounds a little off to me. If I'm not mistaken, the focus of the Turkish question is where (to), not how. My translation would be "Where are we taking the train to?" It's rather informal, but, to my ear, at least, puts more focus on the heart of the question. And yes, we do say "by train" in English, but more often as the answer to a question such as "How are we getting there?"