Burg Eltz/Cochem/Beilstein/Trier in two days?

You could easily spend 3 days nr Rhine river with a cruise and staying in Bacharach is xcellent. Without. Car the Mosel can be a bit difficult.beistein is a beautiful walk thru fairy tale like village. Half day is vg or have a meal there. Burg eltz Is lovely and interesting and warrants half day. You may find yourself rushing to squeeze in the Mosel. I enjoyed both areas a lot . They would seem on paper to be similiar but really not the same. Your 2 day in Mosel would be a rush and dependent on strict public transport carefully. I do understand how u are wishing to see it all.

Have you thought of what to do with your luggage while taking these side trips, and what is your rainy day plan. Are you planning on going to Trier first, checking in, then backtracking to Cochem? Going to Burg Eltz can take the better part of a day. If it is Saturday or Sunday, you can get a bus from Hatzenport station. If the weather is nice, you can also hike from Moselkern station.

That bus starts in Treis, across the river from the Treis-Karden Bahnhof, makes several stops in the towns, including the Bahnhof, then goes along the river through Moselkern, stopping at the Moselanlage, not the Bahnhof, then to Hatzenport before going the Burg Eltz. Note, none of the train stations along the way has storage lockers. If you have much luggage you probably want to leave it in Koblenz, go to Burg Eltz via Hatzenport (27 min to Hatzenport), then come back to Koblenz and get your luggage. Hint: a Tageskarte (Rheinland Pfalz or Verkehrverbund Rhein-Mosel) would be helpful here.

It is hard to believe that all of Cochem is booked solid, even if you are going over a holiday weekend. There are tons of hotels there in all categories on both sides of the Mosel, many more than in any guidebook. If using a booking engine, they have access to only a few rooms in a hotel. Staying in Trier makes going to Burg Eltz (already not easy without a car) and taking a Mosel boat ride to Beilstein difficult. Trier alone is worth two days. So the problem is that you are trying to fit three different stops into four nights: Rhine River, Cochem and side trips, and Trier. I see three solutions.
First, you could stop in Cochem on your way to Trier, visit Cochem and its castle, and then move on to Trier for the two nights. You need to sacrifice Burg Eltz and Beilstein.
Second, you could try again to get a room in Cochem and leave Trier for another trip when you could give it more time.
Finally, although the German rail trasportation is excellent, with compressed time, it may be worthwhile to rent a car somewhere and drive to Trier, stopping at Burg Eltz, Cochem, Beilstein on the way. You may need to get the car in a larger place than Bacharach.

"It is hard to believe that all of Cochem is booked solid, even if you are going over a holiday weekend."

I once tried to get a booking for one person in Cochem during a festival weekend and was told by everyone that they were "ausgebucht" (booked). It seemed like most of the offerings were double rooms. I eventually found a private room in Treis-Karden, an 8-10 minute, 3,65€ train ride from Cochem. It's also the starting towns for the weekend buses to Burg Eltz. When I arrived in Cochem there were plenty of Zimmer Frei signs out in town. I think that most accommodations in Cochem are Doppelzimmer and hosts are reluctant to rent them as singles, particularly long in advance.

There are lots of small towns with rail stations along the Mosel near Cochem. Look here for a list of accommodations (click on "Weitere information", then on Gastgeberverzeichnis 2014-2015, host list, under "dokumente").

Thanks to all of you for your advice. Car is not an option (don't know how to drive). Bus to Burg Eltz is out...will not be there on Sat or Sunday. As for luggage, I was hoping to leave it at the Hotel in Moselkern as Rick suggests. Hate to miss Burg Eltz (Rick raves about it being his favorite). I am more interesting in Roman sites than wine tasting anyway so I don"t mind staying in Trier instead of Cochem. I was only picking Cochem because it was in between Trier and Burg Eltz, both of which I would like to see. My rainy day plan is to wear a raincoat.

Must I sacrifice something? What if I start out super early? Beilstein sounds great. Burg Eltz too. And I really want to see the Roman stuff in Trier.

Interesting about the booking strategy in Cochem... double rooms being available... that explains a lot. But if it;s that crowded I can pass. The place I was going to stay at is no longer in Rick;s guide book anyway.

I don't know about public transportation options so I'll just throw this out. Yes, beilstein is very cute, but so is bernkastle-kues and it's closer to Trier. Take a look at your options with this.