At Goar or Koblenz

The most picturesque part of the Rhine is just south of Bacharach and almost halfway between St Goar and Koblenz. I would travel north on the river because that's the direction the water flows making it a shorter cruise.

"To get to Bacharach from Bingen, take 15m train..."

MaryPat - as I understand it, the OP is considering taking a cruise boat north from Bingen to Bacharach and beyond it to either St. Goar or Koblenz.

busman - There are no through cruises from Bingen to Koblenz this year. You can cruise from Bingen to St. Goar or St. Goarshausen easily enough, however, and that stretch of the river is the best part to cruise - the rest of it is pleasant but not as scenic or compelling. So no worries. If you want to see Marksburg after Braubach, take the boat to St. Goarshausen, then take the TRAIN from St. Goarshausen to Braubach. Boat schedule is on the next-to-last page of this flyer:

https://www.k-d.com/fileadmin/schiffstouren/KD_Fahrplan_2021.pdf

The 11:15 boat from Bingen gets to St. Goarshausen at 12:50. It's the only through boat in the morning. Take the train after that to Marksburg. You do not have time to cruise and to see both castles in the same day. It may be possible to see Burg Eltz instead if you wish - in this case, get off the boat in St. Goar at 12:40 and take the train from there to Moselkern (change trains in Koblenz) where you will set out on the footpath to Burg Eltz. If you go on a weekend, you may be able to get a shuttle bus to Eltz.

That said, I think Marksburg is your best bet for a cruise + castle tour.

Thank you Russ, I just deleted that part from my post.

Go to Boppard. Take the chairlift to get a great view of the Rhine