Hop on/ Hop off bus or train Options

Are you aware of the German "Länder tickets"? These cover one day unlimited travel in one German "Land" (state).
They are valid on all local trains, buses and city transport (U-Bahn, tram), but NOT on ICE or IC trains. They are particularly good value for 2 or more people, as they are €23-€33 for the first person, and +€5 for each extra person.
There is no need to buy these in advance (no discount for doing so), you can buy from any DB ticket machine

Details here: https://www.bahn.com/en/view/offers/regional/regional-day-tickets.shtml

Plus many "Tarifverbande" have one-day tickets. A "Tarifverband" is a local fares pool system, where all operators (bus+train) use common tickets with common zone-based prices. They operate in most cities+surrounding area, plus many rural "Kreise" (counties)

And finally, there is nothing to stop you just buying tickets for each leg as you go at the station ticket machine; A to B, later in the day B to C, then C to D etc.

I'll let others speak of the logistics, but some notes. Most of the scenic Rhine that people travel of see is between (from upstream down) Bingen and Koblenz, although I would extend the range worth seeing from Wiesbaden to Bonn. Bonn to Cologne, however, is mostly industrial, and although there's some towns worth visiting between Koblenz and Bonn, most of the best scenery is upstream from Koblenz.

Mainz and Rothenburg aren't particularly close. There are no commuter trains that connect them (the kind where you conceivably hop on and off). It's been a while since I last looked up the rail routes to Rothenburg, but just getting between the two would involve a series of ICE and regional trains.

Thank you so much!!
This information is greatly appreciated :)

"...multiple stops in one day, between Cologne & Koblenz..."

I assume you are thinking of overnighting in Koblenz.

So a major issue for you to iron out is what you might do with your LUGGAGE when you hop off in this town or that town. Another issue is which side of the river you want to visit. This map will be an important tool for you. Note that the Bonn-Beuel station is right across the river / bridge from central Bonn:

https://www.der-takt.de/suche/artikeldetails/artikel/rheinland-pfalz-ticket.html

NOT all stations have lockers. If you are traveling very light, you might be fine walking around these towns as you please. If not, any towns without lockers might have luggage storage as an option in the Tourist Information office. You would need to check on that town by town.

"...and Mainz to Rothenburg at the end of May."

(Same comments about lockers.)

It sounds like maybe you plan to cruise from Mainz to Koblenz... not such a good plan, if so. You'd have to spend around 11 hours on the boat, and a lot of that part isn't so scenic.

Your idea of hopping off/on is noble but in practical terms it will be tricky. Also, staying in Koblenz (a mostly modern city) is generally not as scenic or interesting as staying in one of the smaller old-world towns south of Koblenz. If you only have ONE night on the Rhine between Cologne and Koblenz, I suggest doing your Rhine visit as follows...

Day 1:
- Catch a train from Cologne straight to Rüdesheim or Bingen
- Cruise back north to St. Goar (about 1.5 hours) through the most scenic part.
- Park your bags at a St. Goar hotel; see Rheinfels Castle and/or catch a short train ride (5-10 minutes) to Oberwesel or Bacharach, return to St. Goar.

Day 2: Leave bags at front desk. See whatever you didn't see on Day 1. Take your bags across the Rhine on the St. Goar Ferry, then do one of two options...

• board the train to Braubach (about 20 minutes) to enjoy the town and Marksburg Castle; then train to Rothenburg.
• board the train to Rüdesheim (about 25 minutes) to enjoy the town, the chairlift; then train to Rothenburg.

Train tickets: "Länder Tickets" will not cover Cologne > Koblenz or Mainz > Rothenburg. You would be crossing from one Land to another on each journey. You CAN do these segments using a "Day ticket for Germany" on the regional trains only (on weekdays only after 9 am.) Buy it at the station in Cologne.

But if you use my suggestion (Day 1, Cologne > Bingen for example) you might check the Sparpreis option (saver fare.) The Sparpreis would put you on a specific high-speed train (ICE, IC, EC) out of Cologne - you would have to use the train at the time you buy it for, and you would likely have a change of train in Koblenz in order to get to Bingen. If you leave St. Goar that pm to visit Bacharach or Oberwesel, you just buy a normal ticket a the station (just a few Euros each way.)