I'm not sure if it matters in what order you visit the stations in this quest. I rather think it doesn't matter, but the first one will likely be Boneyard Station since the quest starts so close to that one. If you notice, the first 3 people out of 4 at each station say they don't know anything, but the 4th one always has a better answer, the answer that points you to the next station. Are you seeing that?
The very last person to give you a better answer will include a more specific detail which leads to a certain NPC at NCR Train Station.