Also called La Plaza Grande, this became the main square of Quito in the 16th century. Afraid the Incas might poison their water supply, the Spanish set up their own protected well here, and this plaza subsequently became the social center of town. It also served as a central market and bullfighting area. Today, Old Town's main square is bordered by the Government Palace to the west, City Hall to the east, the Archbishop's Palace to the north, and the cathedral to the south.
The Government Palace is the most interesting building on the plaza. Don't be intimidated by the chain-link fence in front of the palace; everyone is welcome to walk inside the main area -- just tell the guard that you're a curious tourist. Once you walk into the main entry area, you get a sense of the Spanish/Moorish architecture. Look straight ahead and you'll see the impressive 1966 mural by Guayasamín, of Orellana discovering the Amazon.
City Hall is probably the least impressive structure on the plaza. It was built in 1952, in the Bauhaus style. The Archbishop's Palace was built in 1852; it was formerly the mayor's house. You can now walk inside and see the Andalusian- and Moorish-inspired courtyard; note that the floor of the courtyard is made from the spines of pigs. This area is now an informal crafts market. The cathedral dates from the 16th century. Inside is a good collection of art from the Quito School, including works by Caspicara and Manuel Samaniego. You can visit the cathedral Monday through Saturday from 6 to 10am. The square is most beautiful at night, when all the buildings are lighted up.