Lausanne and Montreux

Not sure it is worth stopping off, they are very close together, only 20-30 minutes by train.
Past Montreux (east) there is the Château de Chillon, that is worth a visit.

Map: https://map.schweizmobil.ch/?lang=en&bgLayer=pk&resolution=50&E=2542100&N=1147300

I recommend visiting the Lavaux Vineyard Terraces. You'll walk through many charming towns along the way with breathtaking views over the lake.

http://whc.unesco.org/en/list/1243

Vevey is worthwhile, especially to visit the market on Tuesday and Saturday mornings.
The port at La tour de peilz is very beautiful and charming. There's a restored castle which houses a games museum. La tour-de-peilz is about a 10-15 minute walk along the waterfront from Vevey.

http://www.la-tour-de-peilz.ch/officiel/Administration.asp?id=8

There's a funicular just near the train station in Territet, just before Chateau Chillon which takes you to Glion. Very good restaurant at the hotel if you want to dine there, but it's worth the trip either way for the views.