One week itinerary around Frankfurt

Your plans look good. I was stationed in Frankfurt for a few weeks with the US Army and visited all the places you mentioned. Mainz would be nice.

Getting to the Black Forest, Rothenburg and Strasbourg, France would take some time just getting there but it could be done.
Also, consider Trier, Vianden Luxembourg as well as Luxembourg city.
Of course, Heidelberg is a MUST SEE.

Mainz is a nice place, and closer to the scenic Middle Rhine (which you didn't mention.) But you might find yourself taking a minimum of two trains for every daytrip. You may need to do some specific research on town wine festivals. Approximate map link:

https://www.ricksteves.com/travel-tips/transportation/trains/germany-rail-passes

No, you probably don't want the mentioned railpass. You can't really sleep in a rural place for extensive daily train travel. I don't care that much for Frankfurt, but it has superb transportation. Your plans involve a lot of train time.

Edit: Because of a later post, I want to note that we do like daytrips, and do them often. But we try not to spend more than an hour on one train, each direction. We try to sleep three nights in one place. We never sleep near an HBF because that's often the most undesirable location in a big city. I will add that we have sometimes rented a car in Germany because we wanted to make three or four minor visits in one day, which can seldom be done by train. That would only be practical if there are multiple destinations on the same train line.

https://community.ricksteves.com/travel-forum/trip-reports/baltic-germany-fachwerke-landesgartenschau

MAINZ has been both home and and a travel base town for me on many occasions. It is a nice city to visit and to use as a travel base. I often recommend Mainz. HOWEVER, I would not describe Mainz as "small/picturesque/beautiful" in the way that Black Forest towns are. Mainz is an urban environment that houses 220,000 inhabitants.

FREIBURG is slightly larger than Mainz with 236,000.

KOBLENZ is somewhat smaller at 115,000.

With your interests I think BOPPARD - a smaller old-world town of 15,000 on a scenic stretch of the Rhine River - will be a better choice.

This video (in German) provides a good look at Boppard. Boppard's Chairlift ride is great fun. Riverfront hotels and restaurants/cafes, a wine garden, and a clifftop outdoor restaurant (Gedeonseck... take the chairlift ride or hike up.)

Boppard is well-located... Other destinations and handsome old-world towns are very close. Some are only minutes away.

St Goar (Rheinfels Castle) = 10 minutes by train
Oberwesel = 15-20 minutes by train
Bacharach = 20-25 minutes by train
Koblenz = 15 minutes by train
Braubach (the home of Marksburg Castle) = 45-55 minutes with one change of train
Cochem (Reichsburg Castle) = 60-70 minutes with one change of train in Koblenz

Map showing Boppard, nearby towns, railways, river crossings, cruise boat docks:
http://www.loreley-info.com/eng/rhein-rhine/walking-hiking.php

How to get from FRA airport to Boppard: October schedule shows DIRECT RE trains at 7:10, 9:24, 11:24 and later direct trains as well. The trip takes 70-75 minutes. (In between these trains there are other train options with a change of train.)

BTW, All Boppard hotels offer the VRM Guest card (free) for free train and bus travel locally. It's the only Rhine town which offers this benefit.

RHINE CRUISES will be available with this day-cruise company through October 27:

https://www.bingen-ruedesheimer.de/linienfahrten/linie/loreleyfahrt

I second Russ's post. Staying in Boppard is a great location to see many towns and villages you describe that you would like to see. I also think Frankfurt is underwhelming as it is mostly a modern day city.

We have visited Rothenburg many times and very much enjoyed it. We visited Freiburg a couple years ago and liked it. However, neither is all that handy from Frankfurt and even less so from Mainz.

https://int.bahn.de/en/offers

We try to select places to stay and visit based on their closeness to one another, so that we might minimize the time lost to travel.

If you want to stay near Frankfurt, consider visiting Würzburg (+ Rothenburg), Marburg (Lahn), Limburg (Lahn), or the middle Rhein mentioned above.

I you want to visit Heidelberg, the Black Forest & Freiburg (Breisgau) - find a base in that direction.

Regarding base cities & day trips, you have to know yourself. We have not liked taking them. We prefer settling in a place for at least an evening/night. Some of our best experiences are later than we would want to return to a base. Other folks love day trips.

Heidelberg: The old-town zone did not suffer much damage during WW II. It may have the atmosphere you are looking for. I suggest you have a look also at the old-world wine towns which line up north-south between Darmstadt and Heidelberg on the "Bergstrasse." Together with Heidelberg, a stay of 2-3 days in this area would be about right.

https://www.diebergstrasse.de/wp-content/uploads/2020/05/diebergstrasse_holidayroute.pdf

Staying in Frankfurt is a good idea. Transport is easy and there are near-by towns that are quick and easy to get to from here. The city itself is very old and has a lot of historic sites to see. If you have time, the neighborhood of Höchst is worth a visit as it is on the Half-timbered route in Germany. If you are interested in Jewish heritage sites, you will find plenty of those in Frankfurt. Dozens of museums for rainy days too.

Give Büdingen a look, instead of going to Rothenburg. Massive city walls and towers and it wasn't bombed in the war. Only an hour by train from Frankfurt. Stop in at Gelnhausen too and see the palace ruins of Barbarossa.
Limburg, Marburg, Idstein, Michelstadt, Seligenstadt, Bad Homburg, Kronberg are all good day trips from Frankfurt and all within an hour by train.