Italy has an excellent reputation for food, and here in Tuscany, and San Gimignano in particular, you'll find that it's well deserved. If you are looking for somewhere to have a lovely meal and a romantic evening, there are many options.
You can choose the countryside or the historical centre, but everywhere you'll be able to taste the local products and enjoy extra virgin olive oil with the local bread Pane Toscano, or cheese, ham and salami. You have to be slow to understand how important food is in the local culture.
You can also take a cooking class or go to the farmers market to understand what Italians buy and cook at home. The chefs at the restaurants are always happy to talk to you about their recipes.
Remember in Italy that food has a particular rhythm: antipasto, primi (first course), secondi (main course), contorni, desserts, and wine.