Answering this question is difficult because the studies on Mexican culture have been very partisan for the last hundred years. On one had, you have the people who magnify the influence of the ancient cultures of Mexico and minimise Spanish influence, while on the other hand you have the people who claim that Mexican culture is a mostly European culture with some influence of indigenous peoples cultures, and both sides often neglect the influence of black slaves. One important thing to notice, is that modern central and southern Mexico have always been the most densely populated areas, while the north was very sparsely populated until very recently, and this meant that Spanish traditions had to coexist with native traditions in the south, this didn't happen in the north, were the seminomad natives were much more hostile to the newcomers, and didn't mix with them. As a result, modern southern traditions have both indigenous and Spanish influence, while northern ones have mostly European influence.

Let's begin with food. If you look at a map of the biome distribution in Mexico, you will see that Mexico is a very diverse country. From rainforests in the south to deserts in the north, from lowland prairies to frozen mountain ranges, Mexico has almost every kind of biome. That means that Mexican cuisine is actually a collection of dozens of different regional cuisines, often with little in common. Just as European cuisines adopted American crops and products (think Italy and tomatoes, Ireland and potatoes) the Americas also adopted European products. The most important are wheat, rice and livestock. Most Mexican dishes use meats that were never available before conquest. At the same time, traditional sources of protein for ancient Mexicans, like insects, became a taboo during the colonial period. It is worth noting that while Mexican cuisine uses ingredients and techniques that the ancient cultures had used for thousands of years, most of the dishes were invented during the colonial period (1521-1821), and many of them were invented by nuns. As a general rule, southern cuisines have more indigenous influence, while northern cuisine have more European influence. After the pacification of the country in the last decades of the XIX century, immigrants of different origins settled in Mexico, and their culinary influence can be felt in some parts of the country; Arab and Italian in Puebla, Chinese in Mexicali, German in Chihuahua.

Religion. After the military conquest of Mexico, came the spiritual one. The Spanish began the evangelization of the natives, who weren't always too receptive of new ideas. In the early years, many indigenous peoples just assumed that the Christian's God and saints were the same gods they had before, but with new names. It is often said that Mexico's particular devotion to saints can be traced back to this belief. The natives got to keep many of their old traditions, now dedicated to the Christian God but retaining several ancient practices. Eventually, the church stopped trying to make natives forget about it. This led to the emergence of two kinds of Catholicism in Mexico. One that was associated with higher urban classes, closer to European Catholicism, and another one more associated with lower rural classes, with some practices reminiscing of chamanism. Of note here is la Virgen de Guadalupe, a dark skinned Marian Apparition who originated in Spain during the Reconquista and who the natives associated with Tonantzin, the Mother God. Her sanctuary in Mexico City is one of the most visited religious sites in the world, an even surpasses the Vatican City as Christianity's (Catholic and non Catholic) most visited site. Another thing to notice is the famous Day of the Dead (Día de Muertos in Spanish), a perfect example of the amalgamation of native and imported beliefs. The ancient natives dedicated and entire month to celebrate their dead ancestors, and their relationship with dead found a fertile ground in the Catholic festivity of Day of All Saints. Contrary to popular belief, most elements of this festivity can be traced to Celtic Europe, and not to Prehispanic Mexico, however the influence of the ancient beliefs is clear, like the offerings of food and drink, as well as the idea of greeting Death as an old friend and not as an enemy and the general atmosphere of festivity and not of grieving.

Music. As with food, Mexican music and dance can't be considered a monolithic tradition, but a series of musical traditions with different origins. This is where African influence is most felt, as Mexican music, just like the rest of Latin America, has a lot of influence from the black slaves. As with religion, different musical traditions arose in urban and rural areas. The musical traditions of the north were also influenced by Polish and German immigrants who brought accordions and polkas with them.

Plastic Arts. Early colonial art benefited from the native artisans, and used native forms of art to evangelize them. Certain passages of the Bible and prayers were "translated" into pictoric language by these artisans, to help convey Catholicism to the masses who hadn't yet learnt Spanish. As time passed, Mexican artistic production forgot native forms of art and focused on European styles. This tendency remained after the independence. It wasn't until the Cultural Revolution after the Mexican Revolution in the first decades of the XX century that Mexican artists rediscovered the artistic traditions of Prehispanic Mexico. Of note are the murals of Diego Rivera, David Alfaro Siqueiros, José Clemente Orozco and Juan O'Gorman, which are influenced by the ancient murals of places like Teotihuacan, Cacaxtla and Bonampak.

As a side note, Mexico City has a festival like the one in your city.