Christmas Itinerary Suggestions

Your trip is very doable by train. The Wieskirche will necessitate a car or a taxi or bus ride. If you're driving right after an international flight, you may be taking extra risks (jet lag, unfamiliar territory, etc.)

"Day 1-2: arrival and two nights Rothenburg... Day 3-4: Bamberg... I'm trying to avoid changing hotels..."

Wuerzburg (Romantic Road town in Bavaria north of Rothenburg) would consolidate your first few hotel nights and is an ideal base for visiting R'burg, Bamberg, AND Nuremberg (one hour to each by train.) It is also only 1.5 hours by direct train from FRA airport's rail station. Traveling first to Rothenburg would mean a 3-hour train ride on 3-4 trains after your international flight.

Wuerzburg has plenty of services lots to see and do including the Residenz (UNESCO World Heritage site.)
http://www.wuerzburg.de/en/visitors/must-sees/index.html
http://www.romanticroad.com/wuerzburg/sights.htm

You can do day trips from W'burg by train on the inexpensive Bayern Ticket.
http://munich-touristinfo.de/Bavaria-Ticket.htm

Though I like Bamberg, I would replace it with Regensberg (the Altstadt is also a UNESCO World Heritage site). Regensburg Weihnachtsmarkt is my favorite in this region. The Old Stadt is lighted very nice in the evening for the Holidays. The Weihnachtsmarkt is located in three different markets square in the Old Stadt. There is also the Weihnachtsmarkt in the Thurn und Taxis Schloss. You have to pay to enter Thurn und Taxis and it can get very crowded. The Regensburg Weihnachtsmarkt is open every night. Many great cafes, bars and restaurants, more than you'll find in the immediate Nuremburg Old Stadt. Many sights, Churches, Rathaus, Stone Bridge, Wurstkuchl, Brauereigaststätte (Kneitinger etc.) to see.

http://www.knei.de/
http://www.wurstkuchl.de/
http://www.bistum-regensburg.de/bistum/dom-st-peter/
http://www.alte-kapelle.de/
https://hotel-orphee.de/
http://www.datino-online.de/
http://www.cafefelix.de/nc/home.html
http://www.brauhaus-am-schloss.com/

I've been to Regensburg and yes, the Christmas market was unique and very nice. If traveling by train would Regensburg be a good 'home base' from which travel to Nuernberg, Rothenburg and Bamberg is doable?

I have to defer to others as I drive. Maybe another location other then Regensburg as you have been there... From Nuremberg you can probably make Munich, Bayreuth, Augsburg and Landshut too. I will guess you can do the same from Regensburg.

"...would Regensburg be a good 'home base' from which travel to Nuernberg, Rothenburg and Bamberg..."

No, not really. You'd be spending roughly 2.5 hours each way to reach Rothenburg from a Regensburg base. Regensburg to Nuremberg can be done in one hour - but that's using the more expensive high-speed trains - standard fare round trip is E52 each (ouch.) To use the inexpensive Bayern ticket day pass on the regional trains you'd need 1.75 hours each way.

If Regensburg is to be on your list, you can day trip there from Munich more quickly - 1.5 hours each way on the regional trains with the Bayern Ticket.

Here's the German Railways itinerary page. It may take you some time if you haven't used it before but it's very dependable and you can figure travel times, connections, and pricing for whatever journeys you have in mind.

Wuerzburg as a base for Rothenburg, Nuremberg and Bamberg outings works well as outlined above.

Alternatively you can base in Nuremberg and day trip to Bamberg (45 minutes by regional train & Bayern Ticket) or Rothenburg (1.25 - 1.5 hours by regional train & Bayern ticket) but reaching Nuremberg on Day 1 from FRA will take about an hour longer (2.5 hours) than Wuerzburg.