Is about an hour north of Basel near enough? If so, I can heartily recommend Tom’s Hundewelt, in Riegel, DE:
This is one of the few Tierheim to whom I feel comfortable entrusting my challenging mutt Robin Goodfellow. In Tom’s hands I know Robin is safe.
The kennel rooms are very clean, and good sized, and relatively quiet. (Calming music is piped in.) The walls in each dog’s room are solid so your dog isn’t stressed by having to look at other dogs through bars or mesh. Each room has an individual outdoor exercise area that the dog can access directly. Walks and other outdoor exercise (as appropriate for the individual) is given daily.
You can choose to add in training sessions or other ‘individual Beschaftigung’ to the basic package, to make your dog’s stay more pleasant. (Tom runs a Hundeschule, in fact he sort of specializes in behavioral problems.)
I got daily reports from the team, and they were always available to answer my questions while Robin stayed with them.
They were happy to administer Robin’s meds, again something many Swiss Tierheim will not do.
Note the vaxx requirements, scroll down here:
https://www.toms-hundewelt.de/hundehotel/
I don’t know if they are booked out or not this time of year, but you certainly can call and ask. They are quite popular, especially among Swiss dog owners who struggle to find care in Switzerland for their ‘less than perfect’ four footed friends.
Tom is a supporter of various Tierschutz efforts, which makes my heart glad.
FYI, the other place in Germany I recommend is Haüser der Hoffnung, in Bernau - but that is not at all near Basel.
https://www.haeuser-der-hoffnung.de
If you don’t mind the distance, this would also be a good option. Especially if your dog is social with others. They have a very good reputation within the Tierschutz community.
If you let us know a bit more about what exactly your dog needs, perhaps we can offer other suggestions as well.
Good luck, I hope you find the care you need.
ETA:
Have you checked with Tierschutz Beider Basel? They are right in your neighborhood - and have an excellent reputation. In addition to their Tierschutz and community outreach, they also provide holiday care.
Good kennels are like gold dust- and rarely have vacancies in peak holiday periods.