Plaza Murillo is the historical center of La Paz. During colonial times, Plaza Murillo was on the Spanish side of the Prado, and it became the center of the action because it was the main water source in town. In its glory days, the plaza was surrounded by eucalyptus trees and a statue of Neptune. In 1900, the plaza was officially named Plaza Murillo after General Murillo, one of the heroes of the Bolivian independence movement.
On one side of the plaza, you'll find the neoclassical cathedral, which took 152 years to build (1835-1987). The towers are the newest part -- they were constructed for the arrival of Pope John Paul II in 1989. If you want to visit the inside of the cathedral, it's open Monday to Friday from 3:30 to 7pm and in the mornings on Saturday and Sunday.
Next to the cathedral is the colonial Government Palace, also known as the Palacio Quemado (Burned Palace). Originally La Paz's City Hall and now the office of Bolivia's president, the building has been burned eight times. Every Thursday at 9am, you can take 15-minute guided tours in Spanish. Outside the Government Palace, you will probably notice guards in red uniforms. During the Pacific War (1879-84), when Bolivia lost its sea coast to Chile, the soldiers wore red uniforms. Today, these uniforms send the message that Chile must return that land to Bolivia.
Across from the palace is the Congress building, which has a long history: It was a convent, a jail, and a university before a 1904 renovation to house Bolivia's congress. Standing opposite the cathedral and the Government Palace is the 1911 Grand Hotel París, the first movie house in Bolivia.