Romantic road

Rothenburg: quaint in appearance but not so quaint during prime tourist season with large crowds... supertouristy, and it requires no more than a day. Before deciding your destinations and overnight stays, I strongly suggest you read up on the alternatives in this part of Bavaria (Franconia,) which is not well covered in Rick Steves' guidebook. A few small-town suggestions for you to explore:

Sommerhausen is in between Würzburg and Rothenburg on the Main River. (Page in German, just see photos.)
Iphofen is nearby and similarly adorable as well.
Bad Windsheim, SE of Rothenburg, has a wonderful open-air museum.

I like Rothenburg for two nights for its scenic location overlooking the Tauber Valley. We almost always add it to our trips for the nice walks both inside and outside of the wall. There is a wealth of hotels and restaurants. It is especially touristy around the town square but you do not have to spend much time there. Rothenburg is easier to visit by car than some larger towns. Gary

I’d stay 3 nights in Rothenburg. If you want to, you can take a day trip from there to Wurzburg or other town. That’s what we have always done.

...day trip from there to Wurzburg...

That's a really good idea since you already have reservations in Rothenburg. If you are that close, you shouldn't miss Wurzburg.

Since you are driving, if you have the time, consider starting the Romantic Road drive in Aschaffenburg. It has a neat castle and a replica of a Pompeiian (sp?) estate house. Just south of there on the old road to Wurzburg is the town of Haibach and just south of there is the village of Mespelbrun which has been in the same family for four or five centuries. It's still lived in and is surrounded by a moat. A real fairy tale place and tours are usually available. Then it's an easy drive to Wurzburg and the Rothenburg. Do a google search for Aschaffenburg, Mespelbrun, and Wurzburg and see what you think.

If you go to Iphofen, go in the summer. In the fall they roll up the sidewalks and close for winter. We were there last October (2017) in mid-October and the town was literally deserted - there wasn't even a dog on the street. It reminded me of Where is Everybody (Twilight Zone).

A week earlier we were in Rothenburg odT and it was busy, but not too overly-touristy at that time. I really love walking the wall in Rothenburg.

If you enjoy a walled city like Rothenburg but want a little less touristy scene, south of Rothenburg on the Romantic Road, Nördlingen is surrounded by a wall with a Wehrgang you can walk on. It lacks tourist traps like a Christmas Store or C&P museum, but it is a lot less crowded. It also has a church steeple that you can climb for a wonderful vista of the surrounding landscape.

Me, I'd drive down thru Fulda to Wurzburg and avoid the route through Dortmund and Koln to Frankfurt. In September (?) I'd plan to stay in Wurzburg; it's wine season and there's bound to be a fest nearby. If you want small and quaint stay in Kitzingen (just south of Wurzburg).

Two nights in Rothenberg odT should be enough, and you really should visit some of the other towns nearby. Nordlingin (already mentioned) is a favorite of mine, Dinklesbuhl is really good, and nobody seems to go to Ansbach (which was the capitol of Bavaria once) which makes it great for tourists. Bad Windsheim's Open Air Museum is probably closed by then, but the spa that gave the town it's name is open.

You don't say how much time you have, and where you're flying back out of, but September is a great time to spend in Bavaria.

Rothenburg is a one day visit. It is a small town and wonderful, but one day is plenty. Don't plan on staying there. Go down the road some more and visit Donauwurth and Dinkelsbuhel. If you can, go all the way to Augsburg and Oberamergau and Fussen.