There is an InterCity train once an hour from Mainz to Koblenz. Half of these are direct trains from Frankfurt am Main.
These trains take the scenic route through the Rhine Valley, passing by such places as the Loreley, where the legendary Rhine maidens used their lovely singing to lure love-stricken barge captains to their doom, much as the Sirens did in ancient Greek mythology.
Second photo: Burg Katz (the Cat Castle) from the train.
Third photo: The Rhine River from the train.
Fourth photo: A second class coach in the InterCity train on the way to Koblenz.
The wonderfully effecient German railway system (DB), to English eyes anyway, has Koblenz well connected to the rest of Germany.
Lying, as it does, on the Rhine corridor, trains run along both sides of the river in both directions.
Perhaps the most obvious day-trip from Koblenz is to the city of Cologne (Koln). Trains using the right-hand side of the river hugs the riverbank for most of the run, and provides some impressive views. The faster trains tend to use the line on the Left-hand side of Rhine, passing through Bonn.
We decided to take the train back to Rudesheim, so that we could have a view of our trip both from the boat as well as from the train. It worked out very well as each one gives you a different view.