4 weeks in Germany

The Elbe isnt 3 exactly teeming with choices as far as cruise lines go. Viking is your most likely option.
It's difficult to make recommendations for activities without knowing your likes and dislikes. I would suggest looking at a few guidebooks for some ideas, as well as the Germany pages under the Explore Europe section: https://www.ricksteves.com/europe/germany

Hotel Monopol is fine and has a nice old world feel about it, but the location leaves a bit to be desired as it directly outside the south exit to the Hauptbahhnof (main station). I would choose a hotel more in the city center, around the Hauptwache area. Perhaps the Motel One Römer, the Moxy, or Flemings. If you must be near the station, I would choose the other North exit, perhaps Hamburger Hof, Crystal or Flemings.
If you are coming in from the airport with the S-8 or S-9, you can stay on the train 2 more stops and get off at the Hauptwache.

The Green Sauce Festival will be happening at the Rossmarkt in the city center and that is one of my favorite festivals.
As to sightseeing in Frankfurt, tell us a bit more about your interests. Lots of historic sites here to explore as well as dozens of museums.

https://en.wikivoyage.org/wiki/Rhineland-Palatinate

For a river cruise I suggest rivers Rhine, Main and Mosel in your case. Hamburg is known as sea port.

Resommending location for accomodation for Hamburg depends on your plans. With day trips I would use a location which is closer to main station or a nearby station of public transport.

To get sure you will have accomodation in Hamburg better book a hotel, not an apartment. Housing apartments are sometimes rented to tourists only which is illegal in Hamburg. Between booking and arrival it can happen that such a provider of apartments is identified and contacted by the authorities and is no longer offering the already booked apartment. The guests can end up without accomodation upon arrival.

Komoot is a good source to discover and plan hiking tours, routes and tips.

By adding your main interests you will likely get more feedback and travel tips.

I would not suggest near the Hbf for Hamburg, but rather near places like Jungfernstieg or Stadthausbrücke.

For Hamburg, you don't really do river cruises from city to city. But for day trips on the river to see the port, etc. you have two great options: The Maritime Circle Line tours have never disappointed, and they are bilingual (most of the others are only in German) and HOHO. The other option is simply to ride the ferries on your Hamburg public transport ticket. That's what locals like to do on a sunny day. One other option is a day trip to Heligoland. I LOVE this option. There is a catamaran from Hamburg that takes you down the Elbe and then across to the Island of Heligoland, where you can spend some time walking the island's red cliffs, bird and seal watching, and more before heading back. The catamaran offers information on the towns you see along the river as well. An excellent day trip when the weather is good!

Here is a good starting point for hiking routes if that is what you meant: https://www.sh-tourismus.de/en/activities/hiking

If you meant more day tours, then I would actually suggest a walking tour of Hamburg (no specific recommendations). Great day trips include Lübeck, Lüneburg, Glückstadt, Schwerin, and St. Peter-Ording. All can be reached by train, and all are walkable towns (as is Hamburg itself). All are absolutely worth seeing, with either nature or history or architecture contributing to their charms, and all are very different from one another.

Walks along the dikes are lovely--I particularly like the Borsfleth - Glückstadt - Bielenberg - Kollmar stretch north of the river or the Jork / Estebrügge area south of the river. For most of this you don't need a car, though it can simplify things. Biking along the dikes is also amazing.

Also of note in the north are places like Haithabu Viking village near Schleswig or the Lüneburg heath. And of course Hamburg itself is so amazing, I've decided I can spend a lifetime exploring it!

The more specific you are with your likes and dislikes, the better we can steer you into the perfect choices for your interests. Local festivals and events are pretty big at that time of year, with major holidays such as Himmelfahrt and Pfingsten falling during your trip. Lots of opportunities there!

Consider exploring the Rhineland area more.
Take a day river cruise from Ridesheim on the Rhine.
Heidelberg is worth a day.
Farther south you have Strasbourg, France and the Black Forest.

Maybe
Hamburg - Helgoland (Island) and retour? Daytrip.
frs-helgoline.de/en/schedule/from-hamburg-to-heligoland

To get sure you will have accomodation in Hamburg better book a hotel, not an apartment. Housing apartments are sometimes rented to tourists only which is illegal in Hamburg.

Interesting. There were so many listings for apartments on expedia and booking.com. I thought they were all legit. Is it only Hamburg? I made a booking in Koblenz and Passau for an apartment, there weren't many hotels available. Now wondering whether to rebook.

I think he/she‘s meaning „private homesharing“ (Airbnb)
Appartements booked via Booking.com, epxedia etc should be no problem. This should be purely commercial, I think.

Many thanks to all who replied to us. Your comments and advice have assisted us in our planning and we now look forward to our time in Germany. Thank you and best wishes.
Paul & Dagmar

Check the guidebooks. The Städel Museum occupied me for about 3 hours. The archaeology museum is an underappreciated place I went to. I had some marvelous pieces. When I was there was also an exhibit of fragments of objects belonging to prisoners of concentration camps. The Palmengarten was another under-appreciated place I went to. I probably did more rushing around and walking that many tourists. But I remember sitting on a bench in the palmengarten for 20 minutes. I suppose other tourists spent 2 hours each day on average some sitting in restaurants. I didn't eat restaurant food once in my 15 night trip to Germany. The Frankfurt historical museum was another under-appreciated place I went. You might want to start with the coins on the top floor and then look carefully only at parts of the collection otherwise if you try to read everything and look carefully at everything you could spend 5 hours or more here. The Goethe house and adjacent Romantic museum irrationally occupied me for over 3 hours. I have a talent for going to under-appreciated sites and museum. Typical tourists just pick one or two of the most popular places and skip the rest. Also I went to Aschaffenburg; somebody on this or another forum suggested it but I originally assumed I would skip it but realized I had time for it one to 2 days before I went. Schloss Johannisberg has a worthwhile museum inside. You can skip the Pompejanum in Aschaffenburg if you have already been to Pompeii in Italy. There is an archaeology museum in Aschaffenburg that I wish I has gone to instead of the Pompejanum.

Mike L. it is a shame not to have eaten any of the fantastic food in Germany. It is fresh, much of it is organic, and many restaurants only serve local products. The breads, cheeses, the mushrooms, the potatoes, the peaches, strawberries, asparagus, are just some of the items missed. I truly do not understand going to a foreign country and not eating their products. Especially to see the difference between flavorful, fresh and healthy here, and the corn syrup filled, GMO flavorless food in the US. Once you try local fruit here, you will be sad to eat the pretty stuff that tastes like paper in the US.