Coming through Basel Switzerland, best place to rent a car for our time in the Black Forest

(pedantic note - GeNgenbach has an N. If you mean Duisburg in the Ruhr, it has no umlaut.)

Bit of an issue, Gengenbach is at the northwest extreme of the Black Forest, Basel is below. So if you got your car in Weil am Rhein or Freiburg im Breisgau (both good choices for different reasons) you would have a lot of backtracking on your last day. If you get the car in Offenberg which is near Gengenbach you need to get there from Basel and then backtrack to go through the Black Forest high route.

Which do you prefer, Julie L?

If a car is an absolute must then I'd opt for Offenberg, as that is where you'll catch the train to Duisburg.

Otherwise, with only 3 nights, you'd be well served by free local transport. Not taking account your time in Gengenbach itself:

A long, pleasant day can be had between Freiburg and Staufen. Scenic train ride to Freiburg via Donaueschingen, though there is a quicker, more direct route.

Haslach, Schiltach and the Open Air Museum, all close by, can take up a day. Triberg is also close by; the falls are decent enough, the town itself not so much.

Nigel,
Thank you for the pedantic note!
Backtracking is not on the list of things we want to do, so it seems I need to reevaluate our Black Forest accommodations. We are making the trip soon, on 02 June, so it may be too late. If I can't find somewhere else to stay I think we would want to get the car in Freiburg im Breisgau. Not sure what the additional charges would be but perhaps we could pick up in Freiburg im Breisgau and return in Offenberg.
Hopefully a Rick Steves Forum member has been through this and can share the details of their experience.
Thank you in advance.

If you are picking a car up in Freiburg, you can also catch the train from there to Duisburg (direct or 1 change).

I'd stay in Staufen, just down the road.

OK, so now we have OFFENBURG misspelled twice in separate posts by separate posters, heh-heh. It does matter a little if you are buying a train ticket from there to Duisburg...

A look at the DB site turns up DIRECT trains from Freiburg, Offenburg and a couple other places in Germany that are at the edge of the Black Forest. It is not necessarily so, if you want to avoid backtracking, that a return to the pick-up station is a good idea; one can pick up in Freiburg, for example, and return in Offenburg or Karlsruhe (further north) to avoid returning to Freiburg and to avoid the longer train trip to Duisburg. Offenburg, Freiburg and Karlsruhe are on the same train line and both are starting points for a direct train journey to Duisburg (at certain hours.)

Not sure that you are aware of the guest-card that comes automatically and entirely gratis with a stay in Gengenbach - and provides completely free train travel all around the Black Forest as well as some other discounts and freebies. The train ride from Gengenbach to Donaueschingen is recognized as the most scenic train ride in the BF; the Freiburg > Donaueschingen ride is also nice, if not at quite the same level... Several of us on this forum have used the guest-card and speak highly of the experience. I'm in another part of Germany right now and have been traveling free of charge on the local guest card for two days already, with similar outings on Friday and Saturday. Sure beats picking up and dropping off a car, worrying about parking, rules of the road, etc.

If you do end up getting a car, look into the exact outlet location(s) carefully. Not all rental companies have outlets which are right next to the station where you are switching from car to train or vice-versa.