El Paso is still served by Amtrak, on the Texas Eagle and Sunset Limited line and passengers heading our way can stop there, or in Alpine. El Paso's Union Station, located just west of downtown is convenient for all travelers.
The Wikipedia article for the station says this: "The El Paso Union Depot, also known as El Paso Union Passenger Depot, was designed by architect Daniel Burnham, who also designed Washington D.C. Union Station. It was built between 1905 and 1906 and was added to the National Register of Historic Places in 1971."
It is still a lovely place to catch a train!