Take the train from Nyon to Interlaken Ost via Lausanne and Bern. This provides a scenic journey through Swiss landscapes and positions you for Jungfrau access.
CHF 60 (approx. Supersaver tickets can reduce cost), 3h30m
From Interlaken Ost, take the train via Lauterbrunnen or Grindelwald to Kleine Scheidegg, then the Jungfrau Railway to Jungfraujoch for stunning alpine views.
Take a train from Nyon to Saint-Gervais-les-Bains-Le Fayet via Geneva, then a local train or bus to Chamonix. This is the cheapest route for the journey.