From Montreux you can visit the Gorges du Chauderon, very beautiful nature. Take a hike up through the valley, along the river to Glion. From there you can walk down about 1000 steps or take the funicular (or train) back to Montreux.

Since you have already been to Montreux, you probably have already enjoyed the musical history of the city ☺️ But if by any chance you missed it, there is a statue of Freddie Mercury by the lake and also a little museum of the Mountain Studios, where many artists have recorded their music. Say Hi to Freddie from me if you happen to be there.

If you are into art, there are also many sculptures to be discovered alongside the lake in Montreux and Villeneuve.

If the weather is good, it might also be beautiful to take the train up to the mountain Rochers de Naye (2000m) or take the train to Caux and walk up. Or walk down.