1 Mercado Jamaica is a locals market of fruit and where flower vendors buy their flowers for the day. Also a great place to buy your edible cockroaches and other bugs in bulk. Worth the cab ride to the edge of Mexico City
2 Palacio de Bellas Artes is the main performing arts pavillion in the middle of Mexico City. The screen is made from one million small glass tiles from Tiffanys. The building is full of the best socialist art work in Mexico City as well including a 4 panel Diego Rivera
3 Museo Memoria Y Tolerancia is the holocaust and tolerance museum in the center of Mexico City. They do a great job using technology to make understanding events easier. Seems like such an easy thing but I have seen very few museums pull it off. Amazing building and art collection as well.
4 Chapultepec Castle is like recommending seeing the White House in DC or the Empire State Building in NY. Don't pass it up even if the lines are long. Catch the tram up the hill and walk down. This hilltop has been used as the center of Mexico City since the Aztecs and houses an amazing castle as well as the best views of all of Mexico City.