Rothenburg sits in the middle of the Romantic Road, and the most natural day trips follow the same route in either direction — both toward other well-preserved medieval towns and toward the wider Franconian countryside.
Dinkelsbühl (50km south, about 40 minutes by car) is what Rothenburg would be if it were less famous: another walled medieval town with a nearly intact circuit of walls, a fine late-Gothic minster, and considerably fewer tourists. It is genuinely underrated. The town has never been reconstructed after wartime damage because — unlike much of Germany — it was never damaged. No bus tour convenience; a car is the practical way to get there.
Nördlingen (70km south, under an hour by car) is built inside a nearly circular meteor impact crater (the Ries crater, formed about 15 million years ago) and the only town in Germany where the complete medieval walls with all towers can be walked at any point. The round plan of the town reflects the round crater. The Stadtmuseum has a good exhibit on the geological history. Like Dinkelsbühl, it is on the Romantic Road but far quieter than Rothenburg.
Würzburg (70km northwest, about an hour by train) is the regional capital of Franconia and has two things that make it worth a half-day: the Würzburg Residenz, a vast Baroque palace by Balthasar Neumann with what is claimed to be the world's largest ceiling fresco (by Tiepolo), and the Marienberg Fortress on the opposite bank of the Main, looking over the vine-covered hillsides. Good wine bars and restaurants along the Mainkai waterfront.
Creglingen (20km south by road, much of it on the Tauber cycle path) has the Herrgottskirche, a small pilgrimage church containing another Tilman Riemenschneider altar — his greatest carving, many art historians argue, even superior to the Holy Blood Altar in Rothenburg. The church is tiny and the altar is in perfect condition. Worth the trip if you respond to late-Gothic sculpture.