I am looking for suggestions for day trips from Frankfurt using public transportation.
Here goes:
Eisenach (kind of far, but still possible as a daytrip)
Heidelberg and Neckar River Valley
I could go on, but that's enough for one post.
If you have any specific destination in mind, you can get schedules through German Rail; they will often reflect a bus, if necessary.
Tom pretty much covered most of the interesting towns around Frankfurt. Will see if I can add a bit to the list. If you give us your dates of when you will be there, we can give you some festival suggestions.
In Bad Homburg, visit the Saalburg, which is a reconstructed Roman fort. Very interesting. The palace in Bad Homburg is worth a visit too, as it is all original.
Worms is interesting, both from the history of Martin Luther as well as its' Jewish history. The cemetery there, Holy Sands, is worth seeing as it is the oldest Jewish cemetery in Europe. Visit the Mikvah and Rashi House.
A visit to Mainz should include St. Stephens and the Chagall windows and also the Isis Temple ruins. Perhaps the Ancient Shipbuilding Museum too. The Mainzer Dom is magnificent. If you go to Worms you will see how much alike these 2 cathedrals are.
If you go to Büdingen, do book a private tour from the TI, as this allows you to go inside of the massive city walls and up onto the guard towers. Price is very reasonable.
Würzburg could also be a day trip. It is certainly one that I have done on a number of occasions.
Eltville is one of my favorite towns along the Rhine. It doesn't have the massive amounts of tourists, but has a pleasant promenade along the river, lots of half-timbered buildings, dry moat filled with rose bushes, and the Eberbach Monastery is a short bus ride away. This is one of the best preserved monasteries in Germany and one of the oldest.
Make sure you give some time to Frankfurt itself. Lots to see and do there.