National Palace (Palacio Nacional)

This isn't Versailles, but it was the Viceroy's palace during the colonial period, and now is a government building. The best thing is the murals, painted by one of Mexico's greatest and most famous artists. It's free to get in, but you must have an ID on you (no age limit though). These murals are some of Rivera's most famous. The palace has a courtyard in the middle, and the rooms on every floor open out onto the courtyard, so there is an open hallway on the second floor, which you can circulate around to take in all the murals. Brilliant work. At 6:00pm every day, the huge flag in the center of the adjoining Zócalo (main plaza) is lowered, with a military ceremony. The platoon which guards the square and performs the ceremony starts from the Palacio and returns there at the end. The Zócalo is the beating heart of Mexico City and is not to be missed, the Palacio is part of that.