I second the comment about not goint all the way to Genoa. St. Remo is a cute town, with a great market and is an easy day trip from Nice.
I warn you, nothing about June in the Riviera will be leisurely and laid back. The only thing slow will be the movement of trafic from once you hit Beziers. This is when all the Europeans from cold countries arrive. Things are croweded, rowdy, and a very party scene. Not to mention expensive and high crime.
Personally I would focus on the area West of Marseille, and East of Nice (also North). Trafic and crowds will still be a bear but not quite so. Save the Glitzy beach scenes for max one day. (Unless this is really your thing.)
I'm not trying to get down on your trip. I lived and worked in Antibes for 5 years, as much as I like the area summers are hard. (though I spend some of my best summers hiking in the Provence area.) You can pm me if you any other questions. Oh Yeah get your hotel reservations way in advance.
It is pretty though, I can still feel the wind off of the sea coming in the train window.