Rigi Hochflue is the most alpine of the 3 Rigi summits , the only one without a cable car to the top. The summit is pyramid shaped and protected on all sides by cliffs. All the routes to the summit are exposed, but not difficult and offer beautiful views over Vierwaldstättersee.
There is a lovely lake side youth hostel at Gersau if you need overnight accomodation. Also hotels in the region and camping at Brunnen