What's the best day trip outside of Frankfurt by train?

There's not a lot to do in Frankfurt.

Welcome to the forum, Toddlimelight.

FYI "Ms. Jo" will be displeased with your dismissal of Frankfurt.

To your question...

Depends on your interests.

• For a short journey to a university town with lots to see and do, head to Mainz.

• To see a rare combination of natural and human history, visit the Upper Middle Rhine Valley (UNESCO World Heritage site) where you take an awesome river cruise past castles, grapevine-clad cliffs, and attractive old world towns, tour a castle or two, and wander through some well preserved old towns.

http://www.loreley-info.com/eng/rhein-rhine/castles.php
http://www.loreley-info.com/eng/rhein-rhine/city-cities.php
https://www.marksburg.de/en/
https://www.k-d.com/en/

Rothenburg is a bit of a tourist trap and not a convenient day trip from Frankfurt.

BTW, why are you staying in Frankfurt if you don't want to visit the place? Stay in Mainz if that's the case - and you can more easily visit the Upper Middle Rhine Valley from there.

Not so, there is much to see in Frankfurt, just have to know where your interests lie, be they cultural, historical, and know where to track them down.

Regrading the day trip...how long of a radius you want to go?

I would suggest Koblenz, Rüdesheim, true tons of tourists there, but so what, still a lovely place, historical, and a place to view the Middle Rhine, Bad Ems, and the town of Marburg, a famous university town, lovely half-timbered houses (Fachwerkhäuser), the Elisabethkirche, etc. I recommend Wetzlar too. I don't recommend Rothenburg.

We already booked our hotel in Frankfurt so we'll just stay there.

The medieval town of Budingen is a short train trip from Frankfurt and great for a day trip. It has a good bit of it's walls still intact and a lot of half-timbered (fachwerk) buildings, some nice restaurants and shops. It's another one of those photogenic small towns in Germany - like Rothenburg but not as crowded and more like a 'real' town than a tourist destination.

There is a lot to see and do in Frankfurt, you just need to step away from the RS guidebook as it ignores 80% of the interesting things to see and do here.
What are your interests? History, markets, museums (40+), nature, photography, Jewish culture, medieval churches? Frankfurt is also a university town, with the Goethe University (40,000 students) having a reputation as the most beautiful campus. Our neighborhood of Höchst is on the Half-Timbered Route if that kind of architecture is of interest.

Rothenburg is too far for a day trip. Visit Büdingen instead which is only an hour by train. A group ticket with RMV will cost you 28.50€ and be valid for up to 5 people and good all day. Unlike Rothenburg it was not bombed in WW2.

Other good day trips are Limburg, Marburg, Seligenstadt, Eltville and Eberbach Monastery, Mainz or Heidelberg. Hessen Park Open Air Museum is quite interesting as is the Saalburg Roman Fort, both near Bad Homburg.

Events taking place middle to late Sept. in Frankfurt and the region:
* May-6 Oct. Blick Achse, Bad Homburg Kur Park
* 19-21 Sept. Harvest Fest, Frankfurt Hauptwache & Roßmarkt
* 21-23 Sept. 688th Gallus Market, Büdingen
* 26 Sept.-6 Oct. Federweisser Fest, Liebfrauenberg Frankfurt
* 27-29 Sept. Wiesbaden City Fest
* 28-29 Sept. Medieval Fest, Heidelberg, Sunday Shopping

There's enough in Frankfurt to fill two days. The old city center is very charming. My favorite day trips were to Buedingen and to Mainz.