The old town of Rothenburg is small — about 500 metres across at its widest — and almost entirely pedestrianised. Everything worth seeing is within walking distance of the Marktplatz, and the full circuit of the town walls takes about an hour on foot. You do not need any transport within the historic centre; you will need legs.
The train station is immediately outside the Rödertor (the eastern gate of the old town) and a five-minute walk from the Marktplatz. If you are arriving with heavy luggage, there is a gentle uphill slope from the station into the town but nothing requiring a taxi.
For the surrounding area, the most useful connection is the branch-line train back to Steinach bei Rothenburg for onward connections to Würzburg and Nuremberg. Buses connect Rothenburg to the surrounding villages, but these are infrequent and oriented toward local residents rather than tourists. For day trips to Dinkelsbühl or Nördlingen (both on the Romantic Road and also walled medieval towns), a car is the practical option unless you join one of the Romantic Road bus services.
Cycling is pleasant in the Tauber valley below the town walls. Bike hire is available at the station and at a couple of places in the old town; the valley floor paths south toward Creglingen and north toward Detwang are flat, well-surfaced, and quiet.