Rather than just end-to-end on the opposite side, how about getting off somewhere scenic to have a wander along the paths that run up high?
There's a little ski-lift thing at the N end of Boppard, with good views of the railway lines and the river.
Alternatively the Rheinsteig walking route from St Goarshausen takes you up to the Lorelei rock, with equally good views of the notorious bend in the river.
Or closer to Cologne, the rack and pinion line at Königswinter has a cafe at the top with a fine view of the river and trains.
Cable car at Koblenz across the river to the fortress whose name escapes me, also with some views.
Along the Mosel, we've climbed to the castle at Cochem, with distant views of the railway.
Or if you prefer a lazier day, pick a sailing on the Goethe or another boat (discounts for rail tickets), for views of both banks from the water. You have to keep your wits about you if you're photographing the trains though!
Edit: I've posted a fair few photos from most of those places over on RMWeb (same user name, various topic/blog titles, but google my username and some of those placenames and you should find them easily enough).