There is a wealth of places to get good fruit and vegetables in Vilanova, and the market is one of the best places to shop, especially on a Saturday morning.
However, you needn't even go that far from the apartment because there is a great fruit and veg shop just round the corner in Calle Libertat. It always has a great selection and sells good quality produce at the best prices.
Whenever I'm at the apartment I always pop in for a bag or two of something. And the guy that runs it loves to use his limited English, saying hello, thank you and goodbye.