See this thread: Best places to live in Lausanne? (mods - this thread should probably be merged into it).
Many Lausannois are a bit reluctant at the idea if living in Rue de la Borde:many subventioned apartments (= many foreigners with low income or unemployed from Africa, ex-Yougoslavia, Turkey, sometimes tensions between the differents cultures) and the Place du Tunnel just down la Borde is a drug market at night. The street is also very noisy. I would rather advise Chailly (10 minutes from the center, nice, Migros, Coop, bank, post office, restaurants), Montchoisi, Blécherette, Pontaise, and a bit further Prilly and Pully.
Vevey is on the lake and is 13 mins by train to Lausanne (no stop) and there are many trains per hour.
I mean the train is a much better transport compared to a bus who stops at every traffic light