The best idea is to start the day at the Puente de Piedra bridge and head for the Plaza del Pilar square. This is a view that's well worth capturing with your camera, as it includes the basilica of El Pilar, the Exchange building, the Town Hall, the Cathedral and the Seo and a monument in homage to Goya beside the Caesar Augusta Forum Museum. You choose, but if you're short of time, the basilica (you can climb up the tower) and the Seo are visits not to be missed.
At lunchtime, you'll find numerous restaurants in the area around the square, in the Calle Mayor and the Calle del Coso. What are the typical dishes? Borage, 'migas' (fried breadcrumbs) and lamb.
An afternoon of culture and an evening of tapas
Then you can visit the Caesar Augusta Theatre Museum and the Courtyard of the Infanta's Palace (containing paintings by Goya). And if you want to pick up a souvenir, take a stroll down the Paseo de la Independencia.
The best idea for restoring your energy is to drop in to some of the bars in the El Tubo quarter, and follow the custom of 'going for tapas'. This is a chance to sample the specialities in each bar accompanied by a glass of wine or beer. At night, you can choose between the youthful atmosphere in the area around the Central Market or the more upmarket venues in the streets of Francisco de Vitoria, San Vicente Mártir and Cesáreo Alierta.