Located on a peninsula with the northern side making up the Port, Ciudad Vieja is the historical center of Montevideo and was once surrounded by protective walls as a fortress of the Spanish Empire. (In the back of this photo you can see the original entrance - the only piece that remains). Argentine forces under Juan Manuel de Rosas besieged the City from 1843 til 1851.
Ciudad Vieja is the best place to observe the architectural variety of the city (from colonial to Art Deco). Plaza Independecia is a good place to have the cab drop you off. Plaza Constitucion is the most happening for night life, but no one knows it as Plaza Constitucion (ask for Plaza Matriz).