MEXICO CITY ACTIVITIES
Coyoacan, is a sort of the hippie neighbor south of the city—although it's old and upper middle class with straight streets and old churches. The Frida Kahlo museum and the Leo Trotsky museum shouldn't be missed. There are great cantinas here—which have fabulous traditional Mexican food (not tortillas but real food like meatballs, chiles rellenos and spicy yerbas—which you have to try!) Dinner is lunch and it's from 3:30-5pm. Most people only eat breakfast and then a large dinner/lunch. So most places are packed at those times and not very much before or afterwards, except for after 8pm which is when folks go for evening strolls. Late at night Mexicans go to Taco places and eat tacos—so you’ll enviable get some of those too.
Coyoacan is known for Frida Kahlo’s house. She is the feminist painter who married Diego Rivera—the famous muralist. http://www.museofridakahlo.org.mx/ It also has the Leo Trotsky museum, who came to exile in Mexico City because of the Rivera-Khalo’s relationship with the socialist party. He was the Head of the People’s Soviet Army in Russia before coming to Mexico where he lived, and was assassinated, when Stalin became jealous of his popularity. http://museocasadeleontrotsky.blogspot.mx/ It´s really amazing history there between Rivera-Khalo and Trostky and the Russians, etc. If you buy books, I’d suggest a stop to http://www.conaculta.gob.mx/elena-garro/inicio.html which is the modern art book store.
The Centro de Coyoacan has many restaurants, bars, the main church and the municipal building, where we will be married. https://en.wikipedia.org/wiki/Coyoac%C3%A1n It is known for where Hernan Cortes burn the feet of Montezuma the Mexican indigenous warrior looking for gold. San Juan Bautista Cathedral is a beautiful structure for those interested in colonial churches.
Next to Coyoacan is the flower market in San Angel (open 24/7!) and the Saturday Bazaar within San Angel is a place full of interesting cobblestone made streets and old colonial houses. This is a high end neighborhood with cobblestone streets and high end shopping, restaurants and bars. San Angel neighborhood also has the Museo Estudio Diego Rivera where the famous muralist isolated himself to work. Also recommend going there. http://www.estudiodiegorivera.bellasartes.gob.mx/
But in Coyoacan there is a nice food market just a few blocks from the center. Both are nice and historic, full of people and colors and food and stuff that you can only imagine! We now live in front of la Plaza la Conchita (Plaza de la Concepción) which is the block where Hernan Cortez lived and married the Mexican Pocahontas—La Malinche. The church is from the 1520s and was built on top of a pyramid. It's currently being restored.
Francisco Sosa Street in front of the Coyoacan Plaza, which is historic and also in the tourist guide books. On Francisco Sosa (name of the first Mexican researcher on folk culture) street is where several presidents have lived and they actually wrote part of the 1917 constitution (the portion of the land reform). It has cute cafes and restaurants and there is another church Santa Catarina form the 1880s. Los Viveros is the botanical gardens in our neighborhood established by the first Mexican Ecologist Miguel Angel de Quevedo. Also a nice place to walk after being in the city for awhile.
Here is a map of Coyoacan
OTHER AREAS OF MEXICO CITY
Other things to see in Mexico City: include the Teotihuacan pyramids. Like the ones in Yucatan but larger, less tropical, and where more people visit each year. That is at least a half a day or more, because you have to take a bus to the North part of the city.
The National Archeological museum (http://www.mna.inah.gob.mx/index.html) at one end of the Reforma Street is an amazing world class museum for archeology. Nearby is the new Sotamayor museum that has great AUGUSTE RODIN sculptures and the building is a work of art. (It's located in Polanco.) Carlos Slim, the world's richest man, funded the construction and art. Lastly there is the Chapultepec castle which is nice and located near the Archeological museum and near the bosques de Chapultepec (woods-a large park also in the center of the city) where there is lots of entertainment for tourist (boats, zoo, sculpture gardens, modern art museum, walkways, etc). It was built by the French when they invaded Mexico in the 1870s and looks a lot like you were in Europe seeing their castles. https://en.wikipedia.org/wiki/Chapultepec_Castle
There is the Zocalo which is the city center with the government buildings. This is a must see!!! Every main plaza in Mexico like most of Latin America has a church, government building and some of the most historic restaurants and buildings. The Templo Mayor (pre-AZtec city center) which is located there and has a great museum on pre-hispanic art and culture. (http://www.templomayor.inah.gob.mx/english_) This is where Gabriel use to work— at the National Palace). There are several bars that look over the Zocalo, which create a nice atmosphere in the evenings. “Hotel de Mexico,” is a classic where several movies have been produced. There is also Historico Central and a new Best Western next door has a place called the Majestic. These are also hotels that you might like to stay at, but it's not the safest area of the city at night.
In the Centro, there are lots of museums related to Mexican history and specialty museums for kids such as the Museo de Arte Popular (know as "MAP") is fun to see pop Mexican Art. Here is the full list here: http://www.guiadelcentrohistorico.mx/museos The best place to eat/see near the Centro is the Sanborns, which is just in front of Bellas Artes. It's the place where Pancho Villa and Emiliano Zapata met during the revolution and have their picture in a cafe. Also in the Palacio National there is a big Diego Rivera mural which shouldn’t be missed.
The other neighborhoods worth your time include the Condesa (sort of upscale, young folks live in neighborhood like Palermo in Buenos Aires, with lots of cafes and restaurants, etc.) Otherwise there is Polanco, which has lots of upper scale bars shopping, movies, restaurants (sort of like Georgetown). I’d suggest you try to stay either near those neighborhoods or better yet near Reforma (center of the city main street). These are 30 min drive with moderate traffic from coyoacan. Polanco has a bunch of high rise hotels major chains, but the neighborhood is so boring but safe!
Other things to see is the Plaza Garibaldi, which is known for bands of mariachi who sit there to get work. You hire them and they go to your party or wherever and sing for the group. The government fixed up the plaza with a Tequila museum which is nice for visitors.
Also if you come south go to Xochimilco, which is where you can rent boats and drink on them for fun… they play mariachi and have flowers to give to your loved ones.
Unfortunately (for some and an advantage to others) Mexico City is a bit chaotic and no one really (or at least I haven't seen) a place where there are clear directions to anything. Neither to visit one place over another or one way to drive to a location over another. It's often difficult to find what you are looking for and there are many alternative routes. Rather, life here is much more about going and finding the place and the experience doing so. It's not a city/culture that is about setting the plan and going exactly to the address that you have on a map. It's much more about feelings and intuition of the city than the anything else.
Here is a good web site with tourist info: http://www.turismo.df.gob.mx