Traveling from St. Goar to Moselkern

Without renting a car or hiring a driver, the train is the best way. Problem seems to be the timing of the connection at Koblenz Hbf, almost 1 hour. You could take the 7:27 train from St Goar and it is only a 34 minute connection in Koblenz, so it is a 1 hour and 35 minute travel time.

To do this, you will need to buy a VRM Tageskarte for each person for 20.60 EUR per person. That will cover you to and from Moselkern (or anywhere else in the VRM district). If it is a weekend, you could buy a single VRM Minigruppenkarte for 23.60 EUR covering up to 5 people. During the week, this is restricted to travel after 9 am, so then you would not get to Moselkern until almost 11 am.
https://www.vrminfo.de/fileadmin/_processed_/1/d/csm_VRM_Preistabelle_2019_web_d8e8bf2c90.jpg

Thanks so much! I appreciate your speedy reply!

Sorry, but I read from the wrong column. I edited the actual ticket prices.

"In September taking a day trip from St. Goar to Moselkern's Burg Eltz."

You do understand that Burg Eltz is not in Moselkern but an hour's walk through the woods from Moselkern - right?

Note that on weekends and holidays, there is train + bus service to Burg Eltz (which skips Moselkern and the long walk.) The train follows the Rhine to Koblenz, and the Mosel as far as Hatzenport. To find schedules at DB for this trip, enter "Burg Eltz, Wierschem" as your destination. You will find train connections to Hatzenport - and a bus connection from Hatzenport to the castle.

The same tickets described previously are valid for this train + bus trip - and for the return trip as well.

Yes, we read that it's an hours walk. Thank you so much for the Train+bus information, because we are going on a Saturday and that might be our best bet. Thank you!

We are planning on traveling from St Goar to Burg Eltz, need to use up a rail pass day. Is the bus from Hatzenport to Burg Eltz covered by the German Rail Pass?

Is the bus from Hatzenport to Burg Eltz covered by the German Rail Pass?

No, the GRP is a rail pass. In big cities like Munich, a GRP covers the S-Bahn, which is a commuter train run by German Rail, but not the U-Bahn, which is run by the city (also not streetcars nor buses).

The bus from Moselkern to Burg Eltz is run by the local transit authority, the VRM (Verkerhsverbund Rhein-Mose.). A VRM Tageskarte would cover both the train and the bus, but a GRP includes only the train. The bus fare is €3,90/adult, one-way.

You said "we", but didn't indicate the number of travelers. I'll assume two (but the same answer applies to up to 5). A Preisstuffen 9 Minigruppenkarte for 2-5 people will cost €23,60 (~$26), which is probably less than a railpass day for 2 people, so don't use the pass for St. Goar to Hatzenport unless you have no other use for that pass day.