The Grosser Mythen (1,898m) is the most recognisable peak above Schwyz — a sharp limestone wedge that looks almost implausible from a distance. The standard ascent starts from Holzegg, reached by cable car from Brunni above Schwyz, and takes about an hour and a half up a well-marked trail with some mild scrambling near the top. From the summit restaurant, on a clear day you can see everything from the Rhine plain to the Bernese Oberland.
Einsiedeln is not the usual base for this hike — Schwyz town itself is closer — but it is a reasonable day trip by car or a combination of local bus and train. The cable car from Brunni runs from May through October.