Thanks for the report!
Some suggestions:
Bullfights: If one is going to the bullfights, always buy a cheaper seat (if you don't want to splurge) in the "sombrachinesca" (shade) section of the ring; buying cheaper "sol" (sun) seats can expose you to drunk, rowdy behavior including risk of physical harm. I can not emphasize this enough.
IMO, don't bother with bullfights in summer; those fights are the "novillero" (newbie, basically) fights and you might get some truly horrible fights - I attended one where the poor matadór tried for the sword kill over twenty times before they sent the guy in with the puntilla short knife, who then made a mess of the descabellado (they try to stab just behind the skull to sever the spinal cord. When the drag team harnessed the bull to drag him to the butcher out of the ring, he was still not entirely dead.
[Petty crime[/b]: Do be aware, as anywhere popular with tourists, of pickpockets and scam artists. The Zócalo (central plaza, only in México we use the word for pedestal or base because people began saying "I'll meet you at the zócalo" and by use it came to mean the entire central plaza square instead of the base of a monument), historic buildings etc. do have this opportunistic riffraff hanging around.
Chapultepéc park:is especially great on Sundays, with lots of families, balloon and cotton candy salespeople and even the occasional organ grinder. Great people watching!
The zoo at Chapultepéc is not brilliant, but it is old - the precolumbian Aztecs had a zoo / menagerie here.
The Castillo / castle housed the Emperor Maximilian and his mentally ill wife, Carlota. There is some fabulous art to see, including huge pieces made of malachite.
Nearby is the fabulous
Museum of History and Anthropology, with amazing collections and anthropological displays. They brought in village groups to build reproductions of a typical small village, and once the construction was over furnished the villages with items of everyday life, including statues of people and animals at their daily life activities.
Restaurants: there are some Mexican and international regional restaurants worth noting and trying. Too numerous to list here, but check the listings
here at TripAdvisor.com. When I go home, or at least the D. F. and Cuernavaca used to be home, my "Chilangos" family and friends do things like breakfast or lunch at
El Cardenal (regional authentic Mexican food, several locations - the hot hand-beaten chocolate made table side makes your breakfast orgiastic), or maybe to
Puerto Getaria for delicious Basque seafood and wine.