You can jump in anywhere you like, although places near where the steamboats dock are less-than-ideal for obvious reasons. I quite like going to Lutry beach (east of the village centre), where there's also a buvette selling food and drinks, and there's a diving board as well. It's easily accessible by public transit: the beach is just 100m or so from Lutry Rive bus stop. Disadvantages are that the beach area is small and it gets very crowded whenever the weather is nice. If you're there just to swim, however, it's a great spot.
There is a beach in Pully as well, but you have to pay an entrance fee.
Also, anywhere between Ouchy and St. Sulpice (i.e. Vidy) is quite nice. Lots of sand beaches, and it's such a huge area it's not too crowded. We had a big BBQ down in Vidy a few weeks ago and the water was fantastic.
Come to think of it, tonight would be a perfect evening for a swim...
Heather