We were only in Vernazza for 2 days, but visited Il Pirata multiple times. The main guy running the…read morecafe is very chatty and runs the pastry side of the business, while his brother apparently runs the rest of the food menu. Everything we tried was delicious, and appealed to me more than the super-touristy spots further down the road (though obviously most of the clientele here are also tourists). Prices seemed reasonable for the amount/quantity of food. Most importantly, Il Parata sells toilet paper, which proved hard to come by in Vernazza.
Be sure to arrive before 5pm if you want food (outside of cannolis, which were available later).