Gengenbach is a great town and a good base town for visiting the towns you mention and much more in the Black Forest.
Here is the TI office search page with thousands of Black Forest options.
https://www.schwarzwald-tourismus.info/planen-buchen/uebernachten
You do not necessarily have to book at this source - you can usually do that with some other booking engine you prefer, or privately with the owner - but this is no doubt the most complete source for the area you are visiting. If you find a place you like/want, look up their homepage, or search for it at your booking engine of preference.
Found this place in Gengenbach at €50/night / 4 persons using random dates. I'm sure your travel dates will work better for you :)
If you think you might cancel any reservation you make, you must check out the conditions for refund (if any) in advance with the owner. If none are stated, make no assumptions; you have no right to a refund of funds paid and are required to pay for the entire period you book under German law UNLESS the owner has a policy that makes allowances. When I book, I check those things. And I put any place that requires a deposit at the bottom of my list. Many owners do not, and prepayment with private rentals can often be a lot of hassle.
Gengenbach is an old walled town with towers on the scenic Black Forest Railway and one of the KONUS towns which offer free transport on rail and bus.