We will arrive in Frankfurt and take trains south eventually ending up in Strasbourg. We would like to consider the possibility of quaint rail accessible towns between the two.
Could anyone suggest potential intermediate stops?
We have the option of spending a few nights along the way, as long as the towns are accessible by rail.
Tuebingen
Gengenbach
Stuttgart and environs
Baden-Baden
I suggest Rastatt or Karlsruhe.
We would like to consider the possibility of quaint rail accessible
towns between the two.
To me, towns don't get much more quaint than Gengenbach (population 11,000). Tübingen is nice but larger (population around 90,000). The Black Forest railway from Gengenbach headed in the opposite direction of Strasbourg will bring you to more quaint towns. Are you planning for a quick stop along the way or planning to spend a couple of nights at a base and explore? For either, I think Gengenbach fits the bill.
https://www.youtube.com/watch?v=5uvNtuv8euA&t=302s
Stuttgart is a little more out of the way, but it is bookended by gorgeous Esslingen (whose town center was not bombed in WWII because its industrial area was out by the river instead of close to town) and Ludwigsburg (with its Baroque Residential Palace).
I would second Dave's rec for Gengenbach. I based myself there for four nights in May and loved my stay. The town is "chocolate-box" lovely and quaint, but is on a main train route so it's easy to get to other places. I did day trips to Strasbourg and the Vogtsbauernhof (which I highly recommend seeing). The train station is an easy walk from the city center and there is a lot of see and do here.
One other advantage is that if you stay here, your hotel will give you a KONUS pass, which entitles you to free public transportation in the KONUS area. You can even use it to get to Strasbourg, although you will have to pay the add-on fare from the border to Strasbourg, which is around €6.
