Segovia is famous throughout Spain for one thing above all others: cochinillo asado, roast suckling pig cooked in a wood-fired oven until the skin is crackly and the meat falls from the bone. Every serious restaurant in the old city serves it, and it is genuinely excellent — Segovia claims, with some justification, to cook it better than anywhere else in Castile. The traditional ceremony of carving it with the edge of a plate (to prove how tender it is) has become a tourist performance at the famous restaurants, but the food itself remains worth the trip.
The old city also does a solid line in judiones de La Granja — giant white beans from the nearby village of La Granja de San Ildefonso, stewed with chorizo and black pudding. It is hearty, cheap, and exactly what you want after a morning of sightseeing in the cold.