In St. Gallen, the abbey complex (especially the library) gives you something to do on a rainy day, although photography isn't permitted in the library (or wasn't when I was there). St. Gallen also has good rail links to Appenzell. OTOH, if you stay in Appenzell Innerrhoden itself for three consecutive nights in the same hotel, you might (if your hotel offers it and I think most do) qualify for the Appenzeller Holiday Card (https://www.appenzell.ch/en/accommod...iday-card.html) which functions as a local rail and bus pass but has other benefits too.