Hello,
Does anyone know of any thrift stores, consignment shops or antique stores in Basel?

There's lots of antique shops down Schutzengraben near Spalentor.

have a look for "Brockenstube" in Google, also The Salvation Army stores tend to hve a wide variety of good quality bits n bobs.

If you can get to Haltingen, Lörrach, Weil am Rhein, or some other places on the German side, there are PLENTY of places.