The terraced vineyards of Lavaux, overlooking Lake Geneva, were made a UNESCO World Heritage site in 2007. You'll see why as you ride from Lutry up the Route de la Petite Corniche, the Cote aux Vignes and then the Route de la Corniche before a fabulous descent down to Vevey. Then home, along the lakeshore.
As a hardcore roadie, it was my lunchtime training ride while working in Lausanne. But every variation is possible. You can even take the train up to Chexbres from Montreux and ride the route in reverse, downhill all the way. Stunning vineards, lakes, villages and mountains. You'll taste the effort everytime you drink the local white (with perch from the lake or fondue from nearby Gruyere) and it will have been worth it.
You can take the train to Chexbres, but it starts from Vevey, not Montreux. Otherwise this lovely spot is just as Mark describes.