One of several small grocers in Riomaggiore, the tiny Alimentari Franca has slightly better options than elsewhere. You'll find cheeses, nuts, antipasti, fresh pesto, Cinque Terre wines and ghiottina (a traditional Tuscan flatbread), as well as whatever seasonal produce is on hand. It's near the lower end of Via Colombo (no uphill huffing required).
Alimentari Franca
Riomaggiore