We had an extraordinary visit in spring (read “before school was out”) in 2002. The people were quietly helpful; the scenery was beautiful, and the fabled hordes of American student tourists had not yet arrived (though one Australian was on the train with his surfboard.)
We did not get a room in a hotel ahead of time and as a result got the best room of our entire European trip by going to a small real estate office in Manarola and speaking in French (the only common language) with the young employee there who set us up in an apartment with a fully equipped kitchen, bedroom, bath and balcony with a view. With this we were able to prepare inexpensive but wonderful dinners with local produce (and pesto; remember nearby Genoa is the home of pesto) thanks to the bountiful local market and we had perhaps the best time of our trip.
But the real reason to go is the scenery, the people, the seafood, (the espresso), the history and the quiet.