Be aware when you're looking at flats in Geneva that they count the rooms differently!
They count the kitchen as a room so a 2 room flat in Geneva is the equivalent of 1.5 in Lausanne or Vevey.
Flats can be expensive in Vevey but if you shop around you should be ok. I live in La Tour-de-Peilz but lived in Vevey for about 7 years. I like the area (obviously...).
In Vevey I paid 540.- all inclusive for a 1.5 room flat which was fine for the time.
I now pay 1620.-(incl. charges) for a 3.5 room (100m2) flat in La Tour-de-Peilz. It sounds a lot, but there are 2 of us and I'm about a 30 second walk from the lake. It's not the same quality of flat I had in Vevey either.
The problem in Vevey is not necessarily Nestlé employees looking for flats as most of those with families seem to move up to St.Légier, Blonay, Chardonne, Chexbres etc.
The problem is that Nestlé rent all the 3.5 / 4 room flats just in case they have to house employees coming over from abroad for a few months. Sometimes these flats are empty for months but Nestlé don't let them go. This means that for the Veveysans who are not with Nestlé, it's almost impossible to find a flat of this size in Vevey and the prices have gone up over the last few years as there are fewer and fewer available.
You never know, you might get lucky.
Good luck, if I hear of anything, I'll let you know