Request help with planning our time near Rhine River

Mainz is a nice city but if you're looking for a small old-world-town experience in great scenery you will want to base yourselves instead in St. Goar (or possibly Boppard.)

You "are taking a train from Munich to Mainz on June 6th..." Not clear whether that's a tentative plan or you already have that ticket or a rail pass. You might want to continue past Mainz to Bingen Rhein Stadt by train instead, which is just a short distance further. From there, walk to the KD boat dock and cruise your way to St. Goar (or Boppard) on either the 14:30 or the 16:30 boat. This is the most dramatic way to view the Middle Rhine castles, vineyards and towns for the first time. (If you need a ticket, the price to Bingen is likely to be the same as the price to Mainz.) The cruise fare is €16 each after your 20% discount (show your train ticket at the Bingen kiosk.)

I'd book June 6-8 in St. Goar. It's easy and cheap to get around from there to Braubach, Moselkern (the Burg Eltz train stop,) and Boppard.

Use a VRM mini-group ticket (€22.10) on one day for the train to Moselkern and back. Buy from a ticket machine and use after 9 am; the same ticket will get you to Cochem as well, if you wish.

The same ticket will work for you on the other day for the ferry crossing to St. Goarshausen; the train from St. G'hausen to Braubach; the train from Braubach to Boppard (change in Koblenz); and the final leg back to St. Goar. You can do the reverse order as well if that works for you better.

On June 9: You can visit Bacharach and/or Oberwesel on this day, nice towns 5-10 minutes south of St. Goar. After that, you might visit Rheinfels Castle in St, Goar, or head to Mainz, possibly with a little sightseeing and shopping there (leave bags in station locker.) The Rheinland-Pfalz ticket day pass is €29/2 and will cover St. Goar - Bacharach/O'wesel - St. Goar (for bags) - Mainz (leave St. Goar after 9 am with this ticket.)

From Mainz to FRA takes 25 minutes by direct train. The R-P does not cover this trip but the cost is only about €5 each for a normal RMV ticket. There are plenty of trains.

Wow, thanks for all that useful information. Unfortunately, I did buy our train tickets already from Munich to Mainz. But perhaps I should just pay extra to continue on to Bingen Rhein Stadt instead. That sounds like it would make for a better trip for us. Hopefully, I can find a place to stay on such short notice in St. Goar.

Thank you!

I believe the Mainz-Bingen fare is €7 each bought at Mainz station.

Boppard would be a good 2nd choice alternative to St. Goar for your destinations.

Here's the most complete set of options in St. Goar to my knowledge:
https://www.st-goar.de/612-1-host-directory.html

There are lots of quaint towns to visit on the Rhine, not just the top 4 that people usually list. Towns like Eltville, Lorch, Assmanshausen, or Oestrich Winkel. Eltville is my favorite, and the near-by Eberbach Monastery is an extra treat. All are accessable by train or bus.

There is nothing wrong with staying in Mainz for at least a day. There are a lot of sites to visit here, like one of the older and very important cathedrals in Germany, the Chagall windows in St. Stephens, the Roman Isis Temple ruins, the Gutenburg Museum, etc.

"Are there other or different places we should see near this area?"
Jo is right, of course. There are many nice towns to visit in the area - and with 3.5 weeks you might still have trouble enjoying all of them. Trier, Linz am Rhein, Limburg, and Bernkastel, in addition to the east-bank towns Jo mentions, are places you might pencil in for a return trip. But with a few days, it's always a matter of making time for your stated places of interest and seeing what's left. Even 2 full days in Mainz would go quickly - there's a lot one can see and do there - but while Mainz has a smallish "quaint" zone, the rest is mostly post-war construction, and the Rhine towns you picked are better located for outdoor activities, Burg Eltz and other castles. However, if you find yourself with time on your hands on your last day, Mainz is a very good idea - it's right on the way to FRA, and it has lockers to stow bags (the Rhine towns to the north do not.)

Speaking of outdoor activities... St. Goar gives easy access to the Rhine Castle Trail (Rheinburgenweg) on the west bank. There's a particularly scenic trail segment between St. Goar and Oberwesel. Just across the river is the Rheinsteig Trail which connects the east-bank towns. Yes, you could hike around here for days and days, and some people do just that. In Bingen, you can hike up into the Binger Stadtwald (Bingen's city forest) and catch a trail to Rheinstein Castle. In Boppard, you can take the chairlift up, then a short hike to the Vierseenblick (4-lakes-lookout) and around a bit - see the green trail lines on the map here. Biking: Bikes are available free or at low cost at some accommodations, like this small St. Goar apartment I rented a few years back. You might want to scan the St. Goar and/or Boppard options for this feature.

Your dates are just around the corner. I haven't scoured all the options but I happened to notice that the Hotel Sonnenhof in Boppard is available (at a very good price) for your dates in the event that St. Goar is booked. I stayed there a few years back - good location, good, clean rooms, very good breakfast.

Thank you all for this very helpful information. I wish we had longer to see all the places, but we are looking forward to our time there. We found a hotel at St. Goar. I really appreciate all of you taking the time to share your knowledge and experience with us!