Any recommendations? We are looking for a hotel, clean, private bath, hopefully with partking and breakfast in early October.
Here is a pdf file from the tourist office in Göppingen that probably lists every accommodation in the town. The page is in German, but it gives links to the proprieties' websites, which might also be in English. Even if the website is only in German, there is probably an email address. Write to them in English and see if they respond. Hint: "EZ" is a single room, "DZ" is a double room, "mit dusche und WC" means the room has a private toilet and shower, "ohne Frühstück" is breakfast not included.
If you can handle the language, using the town website is far preferable to any booking website, which will only show the most expensive properties, the ones that charge so much they can afford the booking website's commission.
Göppingen is not far from Stuttgart. You might find more places to stay there.