In the city center, you can find many restaurants. Castilla y Leon is known for suckling pig and suckling lamb. In Valladolid, the suckling lamb is more famous, and there are restaurants where you go exclusively to eat lamb and the waiters ask you just for the drinks.
You can also find good places to eat suckling pig.Valladolid has been getting into the tapas culture in recent years. Unfortunately you have to pay for tapas everywhere in Valladolid. There are many cities in Spain where the tapas are for free with your drink. There is a tapas competition between Valladolid bars that is held once a year. It is so successful that the Council created a national competition in 2005. If you want to visit Valladolid for a weekend it is worth to check when the tapas competition will be held.
You get another good chance at the beginning of September when the festival takes places. All the pubs put bars in the street, and next to the Stadium you can find marquees from different Spanish areas where you can taste all the typical and famous Spanish dishes.
You find good tapas bars in the old part of the city center, but one favorite is in Calle Correos, behind the Council building. This pub won the tapas competition one year.