Mosel Valley without a car

I stayed in Cochem without a car and hiked up to Burg Eltz (not from Cochem), but I am in good shape and didn't mind talking, hiking, and taking the train. I guess if you wanted to spend a week there and planned to see a bunch of obscure sites that would be difficult to get to without a car, then you might be frustrated without one...but if you just wanted to spend a few days, see Burg Eltz and take a boat ride, and you are in decent shape and able to walk a little, there's absolutely no need for a car. If you cant hike up to Burg Eltz you might have to get a taxi up there I guess.

We really enjoyed our time spent along the Moselle. You can travel by train from Cochem to Trier in just over an hour. There are several stops along the way, so you could stop at some of the cute towns along the way. You might check on river cruises where you could hop on hop off also. You will want to review timetables closely so your not stuck in one place for a long time. That applies to Rhine river boats as well. They are not frequent.

I would take a taxi from Cochem to Burg Eltz.

You don't want to stay in Beilstein if you plan to get around by train. From Cochem trains leave every hour or better in both directions all day long from 5 am 'til around 11 pm. It's very easy to plan around an ample schedule like this one. Beilstein is fun to visit by river boat, or you can go by bus, but as a base town Beilstein would mean boarding a bus every time you head out somewhere, then switching to the train. THAT is a strategy for waiting around.

Looking at the departure board from Cochem, there appears to be about 6 regional trains per hour (average) leaving Cochem going either north or south during the bulk of the day, so waiting around a long time is not a problem.

We have stayed in Cochem 2x, once in 2015 and the other in the early 2000's. Both times without a car and loved it. Did a day trip to Trier and loved all the Roman ruins. Also took the train and hiked to Burg Eltz. Not really hikers and it was great. A nice stroll through the woods. One of our favorite activities is we rented bikes for the afternoon and rode south along the river and after about 10 miles or so, crossed at a bridge and came back the other way. Very flat and was fun to stop along the way for a beer, glass of wine, bite to eat, explore, etc. Enjoy your trip! It was very enjoyable!