I think I read where the Baden-Württemberg Länder-Ticket covers a few places in Bavaria. Would this include Rothenburg ob der Tauber since it appears to be on the border? How do I find out which places in Bavaria are covered?
This map will show you the places covered by the Drei-Löwen-Ticket. Rothenburg ob der Tauber is not one of them. Rail access to Rotenburg is only from farther to the east in Bavaria, from Steinach. The Drei-Löwen-Ticket does cover travel from Baden-Württemberg to Nördlingen (maybe this is what you were thinking of) or to Würzburg. It also covers the loops through Bayern from Ulm to Tannheim via Memmingen and from Kißlegg or Kressbronn to Lindau. That is just on the east side of Ba-Wü, on the border with Bavaria.
To expand on Lee's comment, Noerdlingen is well worth visiting instead of Rothenburg, as it is just as attractive while being less tourist-overrun.
Nördlingen was an overnight stop on my Romantic Road trip in 2007 (done entirely with public transportation). In all, I spent 18-20 hours there and hated to travel on. It has a lot of Fachwerk buildings, an almost complete wall with a Wehrgang you can walk on, and a church tower you can climb for a great view of the town and the surrounding area. What is lacks is a Christmas Shop, a Crime 'n Punishment Museum, and a lot of tourists.
Nördlingen lies inside an ancient meteor impact crater, the Ries. The crater walls were used as a training place for our Apollo astronauts. The museum about it was closed the day I was there, but I understand it is interesting.
You can get to Nördlingen by rail from either Aalen, in Ba-Wü, or from Donauwörth, in Bavaria.
The town website list 14 Hotels, Gasthöfe, and Pensionen, all within the walls or immediately outside, most with contact info (website and/or email). In comparison, Booking.com only lists 3 of them, only one within the walls.
Thank you Lee and Philip. Based on your recommendations, I think I will visit Nördlingen instead of Rothenberg.
When I stayed in Nördlingen in 2007, Uli Wenger operated a Gasthof just outside of one of the town gates, right across from the Bahnhof. It was a nice place, and Uli speaks enough Engllish to help you if you need it. He's since moved his operations inside the walls, so it would be a little longer walk, but not too far. His new place is called Wengers Brettl. You could email him directly, or find him on the Nördlingen accommodation page and use the contact form.