recommendations of castle stays on the Rhine

There is a youth hostel, Burg Stahleck, above Bacharach. Rooms book up well in advance. It wouldn‘t hurt to start looking at booking soon.

Schonburg is above Oberwesel

We enjoyed our stay at Castlehotel Schönburg. But we did not have teenagers with us.
Complimentary sherry in the room and the restaurant was fantastic. The view over the Rhine from the room was pretty good too.

Unbelievably, we walked up and got a room. The receptionist was on the phone when we arrived....it was a cancellation. She showed us the room and we took it.
I suggest reserving rooms well in advance.

Jay

Auf Schönburg is very popular and for good reasons. I would not want to make that steep walk from town with luggage. Most people will taxi or drive up.

Burg Stahleck won't have near the atmosphere - and may or may not be jammed up with pre-teen school kids on week-long outings with their teachers. It's unbelievable to us, but German schools, like the ones in the Rhine region, are often in session in July; in 2022, the Rhine schools don't start summer break until the final week of July. Since their outings take the place of the classroom, there's a reasonable chance that one or more classes will by spending the week there with you. Nothing against kids learning and having a good time... but IME any hostel with school group bookings is going to involve some noisy chaos.

Besides the castle-hostel in Diez (nearby Lahn River) I have no experience with other castle-hotels. I've heard some good reports on Burg Liebenstein, across the river and north in the town of Kamp-Bornhofen (almost across the river from Boppard.) If traveling by train, you can catch the castle shuttle from a spot near the Kamp-Bornhofen station (details from the Liebenstein management.)

Another interesting accommodation might be the riverfront wine barrel rooms operated by the Hotel Anker in Kamp-Bornhofen. It's near both the station and the KD boat dock.

I tend to think of castles as better places for touring than for sleeping. For a fine Rhine Castle tour, do pay a visit to never-destroyed Marksburg Castle (in Braubach, north of Kamp-Bornhofen.) There are good hotel and apartment options in Braubach as well.

We stayed at Castlehotel Schönburg in Oberwesel 6 years ago. We really enjoyed it (staying in a castle was a dream of mine). Just the 2 of us, so not sure about adding family, although our room was huge (we had the room with a little balcony overlooking the Rhein, and the bathroom is behind a bookcase - only a bathtub with handheld shower so that was a bit difficult, but worth it, we loved the room). We did have a car, which made things easier. It also cost more than we usually spend, but it was a special anniversary and did include a 3 course dinner.