May 19, 2016 - 9:01 AM
in reply to adunham
As Arno mentioned, both towns are very small and very picturesque. I've been to both and enjoyed them very much.
Stein am Rhein has a well-preserved medieval town centre, which is a delight to walk through. However, if you have been travelling through Germany on your way to Switzerland, and have seen medieval town centres there, you might prefer to see the lovely frescoes of Appenzell - they are very different from most frescoes that I have seen in other places. The Appenzeller cheese is also very famous, so your idea of visiting the Appenzeller Schaukäserei is a good one.
There was a recent trip report on Appenzell, with some photos, that might interest you: