One of the oldest traditional bar offers a local vermouth including focaccia

for a very reasonable price . definitely recommended .

find it here 

Bar degli Asinelli, Via di Canneto Il Lungo, 78R, 16123 Genova GE

Ravioli with classic pesto alla Genovese

at Raviolhouse, Genoa 

or you can always have ravioli in various sauces or a cult nudo, either way Buon appetito