I should have given more notice to this OP sentence:
we’re thinking of heading to either Strasbourg or Freiburg and doing some day trips to Zurich or Basel, areas near Strasbourg. We’re not necessarily looking to visit Black Forest towns.
As someone who drove to the BF from Zurich, this does not make good sense. It's a two hour drive, and the train is almost as long. Why are you "going to the BF" if you don't want to visit some BF towns, or walk in the BF? I can make a guess that you've heard how expensive Switzerland is, but why drive all the way to the BF if it's not "near" Basel. It's easier to be sure you have a Swiss highway vignette if you rent the car in Switzerland. It's a six hour drive from Salzburg to Feiburg. That seems a bad use of limited vacation time.
I did enjoy my drive, and stopped at several interesting places, among them the Vitra Design Campus, Augusta Raurica, Aarau, and Stein am Rhine, as well as visiting the Fondation Beyeler, I guess Basel's museum closest to Germany.
On another trip, we took the train from CDG to Strasbourg, where after two or three nights, we rented a car to spend a week in Alsace. It was too much extra driving, but we wanted to end up in Avignon, where we returned the car before going back to Paris on the TGV However, I do not consider Strasbourg to be close to Zurich or even Basel. While Google Maps is not a very good time estimator, you may wish to do some mileage and rough time-study about your planned trip.
I have NOT been to Neuschwanstein, but you may wish to use the Search box for this newsboard, top center. Some posters find its construction date and interior make it a second-rate castle. There are castles in Alsace, but maybe not as many as the scenic Middle Rhine.
Edit: The Search box will also reveal explicit instructions for the Middle Rhine.
You don't give the childrens' age, but if they haven't seen The Sound Of Music, or learned about Mozart, three days in Salzburg may be too much. It's a pretty place, but who wants to sit on a bus for The Sound Of Music tour? It might be better to allocate some of that time to the Middle Rhine, where they can walk through actual castles, and view them from the KD boat, while eating a sausage (if they won't refuse something other than a bland hot dog!)
