If you want to treat yourself, La Tortuga di Claudio is a gourmet restaurant with fish specialties. Beautiful view and excellent food at a price that is still very reasonable. The restaurant is on the way from La Spezia to Portovenere and you can reach it using public transportation (bus). it is about 100 meters uphill from the main road.
Just 50 meters away from the fresh food open market is the historic underground Trattoria all'inferno. More than 100 years old that serves typical food from La Spezia with large portions and very friendly prices.
There is plenty to do in the Cinque Terre! Great food, wine, hiking between towns, small beaches and much more. See if you can find the spot where Lorenzo proposed to Adrienne! *Do not drive! You have to take the train that stops at each town from the La Spezia Centrale train station. https://www.trenitalia.com/en/services/travel-around-5-terre.html
Porto Venere is a sea village in the province of La Spezia in Liguria. It is located on the southern tip of a peninsula on the western shore of the Gulf of Poets (or Gulf of La Spezia). The surrounding pristine waters feature 3 small islands, called Palmaria, Tino and Tinetto. Follow the link for recommendations on how to get to Porto Venere and how to best enjoy it.
Lerici is a beautiful coastal town with some site seeing opportunities but mostly known for its beaches. This would be an ideal place to visit if you're looking to spend a day relaxing by the water. *Access is easiest by public bus, boat or taxi. You cannot drive there via rental car.
This is one of the many beaches found in Lerici. You can either rent a lounge chair and umbrella for half or full day from Stabilimento Balneare Venere Azzurra or find a spot on the neighboring public beach (free/no facilities). You can find food, drink and coffee at the cabana of the private beaches or go to the Lerici square for a large assortment of restaurants.
Florence is the capital city of the Italian region of Tuscany and of the province of Florence. The city lies on the River Arno and is known for its history and its importance in the Middle Ages and in the Renaissance, especially for its art and architecture. It is about a 2 hour train ride to get to Florence from La Spezia
The enchanting city of Lucca is a real travel highlight in Italy. Situated halfway between the popular cities of Pisa and Florence, this little town is considered to be one of the most beautiful in Tuscany. A walk through the historic old town reveals many beautiful attractions, picturesque alleys and charming squares. About 1:30 train ride from La Spezia.