Cologne or Burg Eltz

"Which do you recommend?" That's like asking for a recommendation for either chateaubriand or Black Forest gateau.

Are you interested in seeing a castle, or are you interested in seeing a major German city with a variety of things to see and do? No one else can help you decide on these to VASTLY different choices.

My only comment is that both Cologne and Trier are a pretty long distance from Bacharach. It's 2+ hours in each direction by train to Trier and about the same to Cologne. You might look into some closer options - there are many. One of them is this open-air museum where dozens of historical buildings from the area have been relocated. This place really opens a window on local life over the last few centuries:

Rheinland-Pfalzisches Freilichtmuseum (open air museum)

I've caught a very early train to Trier from Bacharach (I believe I changed in Koblenz), spent a half day (mostly around the Roman ruins), ate a quick Brat from a street vendor, taken a train back to Moselkern, walked to Burg Eltz through the forest, toured, walked back to the train and trained back to Bacharach in a day. It's a full but functional day.

I think you could use another day to see Koln (again likely changing in Koblenz), see the Dom, Rathaus and wander the downtown area (maybe see the Roman museum), and get lunch. I'd probably opt for a restaurant lunch. I haven't done this as a trip from Bacharach.

FWIW, Cologne has more than you can see in a day. Especially if you like great museums or Roman relics. While I agree with the earlier posts, I would say that the Cologne Museum of Applied Arts alone is better than Burg Eltz. Opinion, not "fact."

FWIW, Cologne has more than you can see in a day. Especially if you like great museums or Roman relics. While I agree with the other replies, my own opinion is that the Museum of Applied Arts, alone, is better than Burg Eltz, pilgrimage site for Seattle-ites!