Frankfurt to Burg Eltz

Are you traveling by yourself or with others? Too bad your not doing it on a Saturday as there is a bus that runs to the Burg Eltz on Saturdays, Sundays and holidays.

If you go on a Friday, you can travel with a German Regional Ticket (QdL is the German abbreviation) after 9 am. Leave Frankfurt after 9 am on regional trains for 44 EUR for the 1st person and 8 EUR for each additional person up to 5 traveling together. Good for the rest of the day.

You could leave Frankfurt at 9:08 going to Koblenz and change to a train to Treis Karden, arriving at 11:33. Taxi-Reuter can haul up and back to the station when you want.
https://burg-eltz.de/en/planning-your-trip-to-eltz-castle/arriving-by-arriving-by/arriving-by-taxi.html
Trains back to Frankfurt later in the afternoon. Takes 2 1/2 to 3 hours back to Frankfurt.

If there are only one or two of you, you might want to use single trip RMV tickets from Frankfurt Hbf to Mainz for €8,70 pP plus a Rheinland-Pfalz-ticket (€25 for one, €31 for 2) from Mainz to wherever you get off for Burg Eltz (Treis-Karden, Moselkern, or Hatzenport). It's a little more effort, but you'll save vs the Quer-durchs-Land-ticket. I did a similar thing when I went from FRA to Treis-Karden in 2008.

BTW, I think it is a little too far for a day trip. If you use the regional trains as described above, it will be a 6 hour RT just to the Bahn station on the Mosel, plus RT from there to the castle by foot, bus, or taxi just for a 35 minute tour.

I visited Burg Eltz a few years ago. It's a really nice castle...from the outside. (I didn't bother taking a tour of the inside.) But for me, a part of the experience was simply hiking from the little town of Mosselkern (where I got off the train) up through the forest to the castle. It's a pretty but easy hike. I guess castle buffs might find visiting this one an essential experience, but it would never be worth 8 hours to me, not even close.

Much closer and much simpler to reach from Frankfurt is Marksburg Castle. Burg Eltz is somewhat gussied up with furnishings from different periods and thus does not have the same authentic medieval feel that you will experience at Marksburg. You'll have some stunning views from Marksburg as well. Rick Steves tends to get a little overly enthusiastic about his personal favorites, and I know Eltz is a big deal for him, but I don't think you'll be disappointed with Marksburg. English tours are at 1 and 4 pm.

https://www.marksburg.de/en/circuit/

Marksburg is in Braubach - which is just south of Koblenz on the Rhine. The station is right in town. This town map should make it very easy. DB = train station.

emsherman, I like Rick Steves' books, but (while your OP is short and to the point) it's unclear if this is the best use of your time. If you have never taken a KD boat from Bingen to Boppard, this might be a much more satisfying look at a large number of castles. And as noted in a previous, you can go inside one if you really want to do an interior. You can read more about the boat ride by searching this board (top center or top left) for "Middle Rhine".

We went to Burg Eltz by car, but I suspect that even by public transportation, this boat ride may take less unproductive travel-time. I was underwhelmed by the interior, because of so many modern furnishings. However I agree that, on a nice day, the exterior and the hike would be attractive. It's up to you.