The Cordeliers Cloister is a ruined Franciscan complex just inside the old town, all pale stone arches, open sky, and ivy-softened walls. It is atmospheric even before you learn that the underground galleries are used for ageing sparkling wine.
That combination makes it a very Saint-Émilion stop: medieval ruin above, limestone cellar below, glass in hand if you want one. It is less solemn than the monolithic church and a good place to reset between steeper lanes.