For activities, the times will often depend on the activity and fairs or celebrations, etc.
For food blogging, there’d be no best or worse time in Mexico City, unless attending a food event. In other parts of the country there may be scheduled events and using Google should help reveal these.
Some food specialties are restricted by Seasons, however. I happen to like some of the traditional foods, so if I want to eat fresh ant larvae (Escamoles) tacos, the rainy season it is. If Huitlacoches (corn smut fungus or “Mexican truffle”), the same.
One guide is Saveur’s Guide to Mexican food festivals,
here.
Escamoles and many other foods are described at EatYourWorld, as
here.
If you want more Continental, fusion or ethnic foods (mole in Puebla or Oaxaca’s food) there are plenty of resources. Mexico City has some top eateries (Pujol, etc.) and many cities and towns have excellent restaurants offering local specialties, fusion, etc.
And yes, there are Restaurant weeks with associated food events, such as the one in Puerto Vallarta listed
here.
Photos include Huitlacoches still on the cob (Great in crepes, among other preparations), and Escamoles prepared to eat as tacos.