Need the right route

Cologne, Dresden, Prague, Vienna, Salzburg, Munich and some sights in Switzerland.

Just arrange for 5-6 hours of sightseeing in Cologne on your final day there... then take a mid-afternoon train from Cologne to Dresden. Leave around 3 pm, arrive arround 9 pm. Have dinner on the train, or arrange a layover at Berlin Hbf for a meal there on the way.

Perhaps arrange a flight from ZRH or GVA to Paris at the end.

Why don't you fly into Vienna and travel back from this end? FRA is really meaningless for the named plan.

Black Forrest is fully away from everything you mentioned.

Dresden is less a problem compared to Cologne or mentioned FRA.

You are right, I grabbed a good deal on flights. But there is a significant charge to change them. Lesson learned there.
So, since Frankfurt isn't somewhere really want to see, would it make more sense to run up to Cologne for a day, then travel south and loop counter clockwise up to end in Dresden?

I'd be tempted to drop Cologne, much as i like it. You will go from FRA to Cologne from the airport, then go back to Frankfurt to continue your journey. Nonetheless, I'd do it clockwise like this:
Day 1 train to Cologne
Day 2 Cologne
Day 3 train to Dresden
Day 4 Dresden
Day 5 Dresden
Day 6 train to Prague
Day 7 Prague
Day 8 Prague
Day 9 train to Vienna
Day 10 Vienna
Day 11 Vienna
Day 12 Vienna
Day 13 train to Salzburg
Day 14 Salzburg
Day 15 train to Munich
Day 16 Munich
Day 17 Munich
Day 18 train to Luzern
Day 19 Luzern
Day 20 train to Paris
Day 21 Paris
Day 22 Paris
Day 23 Paris
Day 24 fly home

If I figured that right, arrive on Aug 27 and depart on Sept 19. Adjust number of days at each stop as you like.

That makes sense, thank you. We will fly to Paris and possibly find a quick flight across from Cologne to Dresden, only because I can't seem to find one fro Cologne.

Is there a point you would recommend fitting in a river day cruise or two?

I thought you were flying into Frankfurt.
You could put a Rhine cruise into the mix by incorporating that into the trip from Cologne to Dresden. Train from Cologne to St Goar and take the 10:55 K-D boat to Assmannhausen. At Assmannhausen, train to Frankfurt Hbf, then train to Dresden. Gets you to Dresden by 7:39 pm.

I have visited Cologne and enjoyed the cathedral. However, Cologne is a bit out of the way considering you planned cities to visit. Consider skipping Cologne for this trip.

Sam, are there options for a cruise that people can just do for a night or two? Most places I've called have a minimum of 8 days booking.

For those recommending to skip Cologne, you are wise. Is there another Cathedral on our route with that depth of history and architecture you would recommend?

Sam, are there options for a cruise that people can just do for a
night or two? Most places I've called have a minimum of 8 days
booking.

Apparently you are calling companies that sell multi-day cruises internationally.

There are LOCAL cruises which take you through the most scenic part in a couple of hours - like the one Sam referred to from St. Goar at 10:55, which is operated by K-D cruises:

Scroll down for the full schedule of boats: https://www.k-d.com/fileadmin/KD_Fahrplaene/KD_Fahrplan_intern_2024_web.pdf

https://www.k-d.com/en/

Don't prepurchase tickets. That will not get you a reservation or a seat. Just show up at the St. Goar dock, buy a ticket there and ride to Bingen. You will get a 20% discount by showing the train ticket you used to reach St. Goar.

Brilliant! Thanks everyone.

Well, while you are Paris you can take a day trip to Chartres for probably the most iconic Gothic Cathedral of all.

While the Cologne Cathedral is stunning, the facade and towers are fairly modern, started in 1842 and completed in 1880. When Cologne went to Prussia after Waterloo, the King of Prussia decided it would placate his new Catholic subjects if he got it funded. When he became Kaiser of the new Germany in 1871, the project really took off.

Yes! We missed Notre Dame when we visited in 2019. We are intending to fly over to Paris after we finish in Germany, but it looks like a train might be a good plan? We don't mind a couple of additional quick flights as needed to save time.

Hmm, but I wonder how "quick" those flights would be. The only candidate I see would be Frankfurt to Dresden, as there are direct flights. With a flight, check in at least 90 minutes before the flight, 1 hour in the air, at least 30 minutes to deplane and collect luggage. 20 minutes to take train into Dresden. 3 hours a 20 minutes total. There are direct ICE trains from Frankfurt to Dresden in 4 hours and 20 minutes. So you went through all the hassles of flying to save 1 hour. On the train, get up and walk around when you want, go to the bar car for a drink, or bring your own.

You've got us think, think, thinking like a pooh bear. Thank you!

There are great cathedrals in Prague, Vienna, Salzburg and Munich. Also, in Mainz, Aachen and Ulm.