This has been surprisingly complex to research, but I believe the answer is a passenger station in the middle of Elysian Fields Avenue, just north of Decatur St. See this 1878 map: http://cartweb.geography.ua.edu/lizardtech/iserv/calcrgn?cat=North%20America%20and%20United%20States&item=States/Louisiana/Louisiana1878c.sid&wid=1200&hei=900&props=item(Name,Description),cat(Name,Description)&style=simple/view-dhtml.xsl

That station would have served the New Orleans, Mobile & Chattanooga Railroad. The map shows various railroad depots on the riverfront, but I think those would have been for freight rather than passengers.

Here's a map from 1865, on which the Mobile line is shown as projected. It's not entirely clear that portion was complete in 1870, but it seems likely. The earliest Official Guide online is 1881, and it suggests that the most likely routing from Maryland would have been via Chattanooga rather than than Southern Illinois.

Can you clarify your question a bit more? Are you asking where the various railroad stations were located in New Orleans circa 1870?

I'm sorry, that should read, "Where IN the city is my train station?" I have found references to a station on Basin Street, but not a 'named' reference until later on. At I found one statement that mentioned a station on Canal St, but I couldn't match it with a date.