My suggestions would be:
Heidelberg or Baden-Baden if you choose the Black Forest route, or
Riquewihr if you go through Alsace.
They are all charming and worth a couple of nights. I particularly like Riquewihr as the town itself is very pretty. It is also near Mulhouse, Colmar and Strasbourg. Mulhouse has a great car museum with many Bugattis and other interesting makes. Colmar and Strasbourg are as pretty as Riquewihr. So Riquewihr would be my first choice.
Both routes, Alsace and Black Forest, will take you to Nurburgring through Koblenz. From Koblenz I would recommend a detour along the Mosel to Cochem before heading for Nurburgring. The road along the Mosel is very scenic and runs close to several castles.