is Rothenburg a good home base for 3-4 days on Romantic Road

We lived in Augsburg, on the Romantic Road for four years. It is a wonderful city and worth a full day to visit.

As for staying in a city and using it as a base, I think this is not a good idea. The road is quite about 200 miles long and is best toured in a rental car from one end to the other. You can do the entire road well in 4 days. Cities like Wurzburg, Augsburg and Fussen/Garmisch need a minimum of a day. The smaller towns like Rothenburg, Nordlingen and Dinkelsbuhl can be toured in 2-3 each.

I suggest starting in Wurzburg and stay in either that city or Rothenburg the first night. After touring Rothenburg, visit the other small walled cities and stay in Augsburg the next night. Then proceed to Fussen, stopping in Oberammergau, home of the famous Passion Play.

End your Romantic Road in Fussen and do the castles and the Zugspitze near Garmisch.

You need two base towns.

There are towns in between Würzburg and Rothenburg on the Main River which you may wish to visit... see links below for 3 of them:

https://www.youtube.com/watch?v=VLUgpoQIFHI
https://www.youtube.com/watch?v=0AeGts3FIZA
https://www.visitochsenfurt.de/en/medieval-town-germany/

Ochsenfurt and Marktbreit are members of the German Half-timbered Road, Franconian branch:

https://www.deutsche-fachwerkstrasse.de/en/Routes_Cities/Franconia.html

Bad Windsheim is too. Fantastic open-air museum there.

Like these, other very nice places nearby often get overlooked by Romantic-Road-bound visitors who stay in Würzburg and Rothenburg. Maybe they figure that if they were really good, these other towns would be right on the Romantic Road Flawed thinking, IMO. They probably aren't aware that RR towns pay the RR organization a fee for membership and its marketing services.

• The German Castle Road is another theme road... besides the castles, its destinations include Bamberg, Nuremberg, Coburg and Bayreuth which are all pretty awesome and include UNESCO World Heritage sites. Many of the other Castle Road stops are wonderful too.

https://www.burgenstrasse.de/upmedia/Uebersichtskarte_Burgenstra%C3%9Fe-und-Europa.jpg

• The German Half-timbered House Route has other branches near Würzburg too; Miltenberg, Michelstadt, and Wertheim are closest:

https://www.deutsche-fachwerkstrasse.de/en/Routes_Cities/From-the-River-Rhine-to-the-River-Main-and-the-Odenwald-Forest.html

So I wouldn't necessarily limit myself to the RR choices. You might just find something else nearby that suits you better.

Rothenburg and Fuessen

Thank you for all your input. Greatly appreciated.
One last question. When spending time in zugspitze how much time should you stay and any suggestions on what to not miss.
Thanks again

You go up to the top of the mountain (Zugspitze) via either the cog train or the cable car. Once up at the top, you will probably spend no more than a hour, unless you can ski on the glacier. Total time will depend on which way up, I think the cog train is a bit slower.

"When spending time in zugspitze..."

"Zugspitze" is the name of a mountain, not a town. Are you asking about things you don't want to miss in Garmisch-Partenkirchen?

In 2008, I did the Romantic Road with nothing but public transportation, a few trains, mostly buses. I did it south to north. I started at Wieskirche because I had already been to Füssen multiple times. I stopped at Schongau, Landsberg¹, Donauwörth, Harburg, Nördlingen¹, Dinkelsbühl, Feuchtwangen¹, Rothenburg, Weikersheim¹, Bad Mergetheim, and ended in Würzburg. ¹ indicates overnight stays. I only had lunch near the Bahnhof in Rothenburg because, again, I had already been to Rothenburg multiple times.

The Road itself is nothing special, in fact, it was clogged with cars, buses, freight trucks, and farm vehicles. It's the towns along the road that rate the time. I would spend four night evenly spaced timewise by how much time you want to spend in the towns.

I was pleasantly surprised by Landsberg, absolutely loved Nördlingen, was not so enthusiastic about Schongau and Dinkelsbühl.