Heidelberg or Rothenburg ob der Tauber?

I enjoyed both, but for a day trip from Frankfurt I would choose Heidelberg. If you are taking public transportation Heidelberg is easier to get to. If you are driving you can take the Bergstrasse at least for part of the way which is a beautiful drive. I really enjoyed Rothenburg in the evening when it was less crowded and there was the Nightwatchman's tour. Heidelberg has a nice old town, and really pretty views from the castle terrace, on the bridge and while walking on the Philosopher's Way.

Your two choices aren't really comparable.

Heidelberg = pleasant city of modest size, about 2 hours round trip travel
Rothenburg = very atmospheric old-world town but very touristy, 5-6 hours of train travel.

It's unclear to me why these two are your only options. GELNHAUSEN is only 1:10 round trip from Frankfurt by direct train. The old walled town of BUEDINGEN is a fine alternative to the theme-park feel of Rothenburg and only about 15 minutes beyond Gelnhausen. You could do a two-fer in a single day trip.

MAINZ, a university town, is an unheralded place on the Rhine River with a nice pedestrianized old town zone, not terribly different from Heidelberg in size and charm, and with several good sights - and it's less than 1.5 hours from Frankfurt round trip.

Similar to what Russ said. Rothenburg is not what I would consider a day trip at all. A visit to Büdingen would be at the top of my list instead. It is only an hour train trip from Frankfurt with just one easy change at Gelnhausen.

I like Heidelberg a lot, but it is completely different from a medieval walled town.

If you do choose Büdingen, I recommend booking a private tour with the TI. They only charge 41 € I think, but they take you inside of the city walls and you get to climb up on top of the Witches Tower as well as into its' depths.

http://www.buedingen.info/

Thank you all for the suggestions!
Rosa