The Riviera police webite has maps of all parking including where the free spaces are in Vevey and Montreaux at
http://www.police-riviera.ch/qsPorta...p?N=3384&M=110

Click on "Le stationnement à Vevey" and "Le stationnement à Montreux" respectively.

Haven't checked if there is something similar for Lausanne.

Just because there are gratuit car park spaces available doesn't mean they are libre though!