3 days in Germany

The holiday is on the 3rd, not the 2nd. After a trans-Atlantic flight, just enjoy your arrival day in Frankfurt and move on the next day. Great farmers market on Thursday in Frankfurt at the Konstablerwache. Tons of history in Frankfurt for all different eras.
Local towns to visit - Büdingen, Marburg, Limburg, Seligenstadt, Idstein, Bad Homburg
Tourist attractions will be open on the 3rd as well as restaurants and museums. Just stores are closed.

This is what is happening in Frankfurt.
Federweisser Fest, Frankfurt Liebfrauenberg – 28.09-5.10
Jazz on the Römerberg, Frankfurt – 3 Oct.
Antique Market, Frankfurt Konstablerwache – 3.10

You may find either Bingen or Bacharach on the Rhine of interest.

Bacharach and St Goar.

The reason you are getting suggestions like Bingen, Bacharach, and St. Goar is that these are small wine towns that are separated by only a few miles and situated in one of Europe's most scenic river valleys... AND because they are quite close to FRA airport AND on the route to Amsterdam. It's a place where Germans, the Belgians and the Dutch often go to relax, enjoy the outdoors, and try the "mighty fine wine" from some of Germany's most popular wine regions. The entire stretch of river between Bingen and Koblenz is a scenic playground dotted with medieval castles, half-timbered old-world buildings, vineyards, biking/hiking opportunities and more. So it's kind of a complete no-brainer based on your interests.

Area map

Scenery near St Goar

Cruise boat in Oberwesel w/ Castle-Hotel Schönburg

Marksburg Castle in Braubach

Old-world streets and buildings in Braubach

Weingarten in Boppard

Aerial view of Boppard with cliffside vineyards

Gedeonseck terrace with view, near the top of the chairlift in Boppard

A car is not needed to visit. Probably not a good idea for wine-sippers anyway. Wineries are in town. Trains, ferry crossings, and cruise boats have you covered here on both riverbanks, and you can leave the area easily for Amsterdam from any train station:

http://www.loreley-info.com/eng/rhein-rhine/walking-hiking.php

Also, if I were going to Munich for a short stay, I would fly into Munich, not into Frankfurt. I personally don't consider Oktoberfest a must-see. There's a good chance you can still find some very local wine festivals in early October, which will be almost as festive, but without crowds, drunks, and extra charges.

The scenic Middle Rhine gorge is an excellent suggestion (by previous replies.) And it's nearer Frankfurt. There are also lots of pretty towns near Frankfurt, for example, the Fachwerkstrasse towns. You can only see a tiny fraction of Germany in 3 days.

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

I neglected to remember that your visit coincides with Boppard's Weinfest. Wine stands open on at 2 pm on Friday and Saturday, with the Rhine in Flames fireworks exhibition Saturday night. Lots of street music throughout the weekend. Admission is free. The small town gets crowded for this popular event, and parking is scarce, which makes getting there by train the smart alternative.

https://www.boppard-tourismus.de/media/download/ti_flyer_mittelrhein-weinfest_boppard_250523_ansicht.pdf

Last summer, my friend and I flew into FRA, got a car (very inexpensive, even with the second driver) and went to Wiesbaden (very close; maybe 45-minute drive) and recovered from our flight in the thermal pools there. Next morning, we drove up the Rhine, across and down the Mosel, where we spent two nights in a fabulous AirBnB in Enkirch. We spent our one full day driving around, visiting Landshut (partially ruined castle with amazing views), eating a massive platter of meat and veggies at this place: https://waldschenke-bernkastel.de. It was glorious. Of course, we were there in July, so in October YMMV, but it seems like it would still be harvest season(?) and maybe you'd have the foliage(?). You can stay at a winery. Be careful not to drive after drinking, as the tolerance there is very low. I was lucky I had a sober driver! We returned our car at FRA and flew out to Belfast. You could do the same but take the train to Amsterdam.

thank you all for so many wonderful suggestions and quick responses! I so appreciate it and have changed our plans to stay in Frankfurt and see the beautiful options around there! I guess I need to come back for more time in Germany!