The number one dish in Valencia is paella. Classic paella consists of rice, rabbit meat, chicken, snails and vegetables. All this is cooked in a large paellara pan (by the way, the rice stuck to the bottom of the pan, socarrat, is a delicacy).
If you get a chance, try agros negre - it is a rice dish of black color (the chef achieves this effect thanks to cuttlefish ink) with shrimps and squid.
Another feature of Valencia's cuisine is the great variety of fish dishes. In Valencia restaurants they cook mullet and eel, cod and monkfish, perch and many other inhabitants of the Mediterranean Sea, generously seasoning the dishes with vegetables and spices. The best place to try "sea" dishes is in such popular Valencia restaurants as El Canyar, Alejandro Del Toro or La Embajada.
Be sure to check out Valencia's orchaterias as well. This is the name given to places where the iconic local drink Orxata is served (by the way, Salvador Dali was very fond of it!).
It is made from chufa, a ground almond, and the drink resembles milk, though it is very sweet. Orchata is great in the heat of summer - it is usually served with ice and powdered sugar biscuits.
Some other local culinary "attractions" are Turrón (nougat made of roasted almonds with honey) and Bunyols doughnuts, which should definitely be eaten with hot chocolate.