As you may know, Italy has a lot of regional food traditions, and anywhere you go you can try a very unique local specialty. It happens with food in La Spezia area too, although the region of Liguria is not so well known for its food.
Pesto is a sauce for any pasta dish, and one of the most known local traditional recipe. One of the most important things to keep in mind to have a good pesto, though, is the freshness of the ingredients. So there is no better pesto than the one you can make at home with some fresh basil leaves, garlic, oil, pecorino cheese, and pine seeds, beaten (=pesto), not mixed, together until you get a vivid green jam. Nevertheless, you will see some very promising fresh pesto sauce jars, sold in the most touristic places; not all of them are bad, especially those that have a short expiring date.
Testaroli is a very local kind of pasta, a simple and poor dish, usually prepared with pesto or some sort of meat and tomato sauces. It is usually sold in a sealed vacuum plastic bag that can be kept for a couple of months, in a round piece: once open it should be sliced in smaller pieces and put in boiling water for a very short time, two or three minutes are enough, then served hot with the above-mentioned sauces.
Spongata is a typical baked sweet cake, excellent thanks to the filling, a sort of jam, preserved among the dough, enriched with pine nuts, almonds, spices, and other flavorings. This cake is more typical of Sarzana, a nice small city about ten miles from La Spezia.
There are of course many “raw” materials produced in this area that are worth a mention: honey, olives, potatoes, sausages, cheese; most of them can be found during an excursion in the Vara Valley, a scarcely populated and very green area, where many farmers grow and breed bioproducts. Lemons are the excellence of the Cinque Terre territory.
Sciacchetrà, legendary sweet wine is a true symbol of the Cinque Terre, today almost impossible to find despite the very high demand. Born in Levanto and produced since a very long time in all the villages of the Cinque Terre from grapes that come from the famous typical terraces and must be hung and dried in the sun to get to the sugar content corresponding to 17º of potential alcohol. These are the characteristics you should look for when buying the Sciacchetrà wine.
Limoncino is a liqueur obtained from the infusion of the most typical lemon peels, water, and sugar. It is very common in the Naples area too, where it is usually called Limoncello. There are many distilleries producing this digestive drink, you should possibly look for those that are made without the addition of dyes and preservatives.