While it's not the most spectacular thing to see in Zaragoza, the Zuda Tower is certainly a testament to the city's impressive history. It was built on the corner of the original Roman wall erected by Caesar Augustus nearly 2000 years ago as well as another tower built almost 1000 years later by the Moors during the era of Muslim rule in Spain. After the Christian Reconquest, it was used as a palace for the Kings of Aragon before they moved to the admittedly more spectacular Aljafería Palace. The took its current shape in the 1500s.
These days, it's a tourist information center and museum that has an amazing view from the top floor. It's located right next to the San Juan de Los Panetes Church on the west end of the Plaza de Pilar.