-We are scheduled to arrive in Frankfurt 9:30 AM on Jun 5
-Stay the night in Bacharach
-Stay in Cochem the following night
-Leave Cochem the following morning to spend a day in Rothenburg
Hi, Joel.
If you arrive on time, you MAY be able to catch the 10:37 train departure for Bingen, arriving 11:31. But there is no KD boat heading north until 14:30. You'll be stuck there for 3 hours. If instead you take the train to Bacharach, you'll get there at 11:50. I don't know whether you can drop your bags at Stahleck castle-hostel at that hour, but that place is 500 stair steps on the way to heaven from town. You may or may not want to make that ascent twice in one day. There are no lockers at Bacharach station if you were to just hang out in the town. So my suggestion would be that you scurry from the station down to the KD dock. That same boat that you missed from Bingen at 11:30 leaves Bacharach at 12:15 for St. Goar (12:55.) (You will miss that first part of scenery that starts in Bingen by boat, but you can still enjoy it from the train window.) It is in fact this part between St. Goar and Bacharach that R. Steves recommends.
Once in St. Goar, walk about 2 blocks into the town center and grab some lunch at one of the cafes there. You'll have a view of Rheinfels Castle if you sit outdoors. After lunch, walk down to the St. Goar TI office on Heerstrasse and ask them to keep your bags (they take lunch from 1:00 to 2:00.) Then have a walk (a more gentle slope, not hard without the bag) up to Rheinfels Castle. Spend a couple of hours there? Fetch your bags. Then catch a train back to Bacharach (a 10-min ride) at 15:56 or 16:56 (takes 10 minutes and €3.90.)
On Day 2: Your one-way fare to Cochem is €20.80. Buy the ticket at a ticket machine in Bacharach. The ticket allows you to get off in Moselkern for several hours to do the hike to Moselkern and back. Then continue on to Cochem. HOWEVER... You won't have anywhere to put your bags while you see Burg Eltz....
For this reason and because it's a long trip from Cochem to Rothenburg, I suggest instead that you NOT sleep in Cochem. When you take the train to Moselkern, you must change trains in Koblenz (which DOES have storage lockers.) So let's say early that morning you see a bit of Bacharach and catch the 10:21 train from Bacharach to Moselkern; you have a layover of 12 minutes to walk down the platform steps and stow bags in a locker there before your train to Moselkern departs (Have your Euro coins handy.) Then you just need to return from Cochem in the evening to Koblenz. Maybe you stay there. Or maybe you catch an evening train to Mainz and stay there for the night. If you take this suggestion, then don't buy the one-way fare that morning - instead, buy the Rhenland-Pfalz Ticket, a day pass which covers the train to Moselkern, Cochem, Koblenz and Mainz, from a Bacharach station ticket machine - only €24 no matter your destination. You'll be a lot closer to Rothenburg if you overnight in Mainz.