Kindly note, the only mountains where the STP grants free access are: Mt. Rigi, Mt. Stanserhorn, Klewenalp / Stockhütten, Stoos, and Rochers de Naye.
For all other mountain trips, the STP grants a reduction being either 50% or 25%.
You can retrieve information on the reduction from the STP validity map, downloadable from the Swiss Travel Pass website: Swiss Travel Pass – the All-in-one-Ticket for Switzerland | SBB → More on the topic. → Map of validity
- Genève to Col-du-Pillon, Glacier 3000: 50% reduction
2. Genève to Brig and onwards to Tirano by Glacier express: 100% coverage
- Genève to Interlaken Ost to Eigergletscher to Jungfraujoch: 25% coverage
A personal side note: If Geneva is chosen as your base, it will entail a considerable amount of travel time, as it is not conveniently situated to explore the Swiss Alps.