Mexico City is one of the largest cities in the world, so you have like a million things to do, from theater to visit the pyramids of El Sol and La Luna. One of the best restaurants in the world is on Mazaryk and it's called Biko, the prices is a little bit over the top, but, believe me, youll never taste anything like that in your life! Now, for more mexican style, you can always go to El Bajio, this restaurant, the original is on the Cuitlahuac avenue. Ask for the Mole de olla, soooo goodd!! 

No matter what you do, mingle with the locals and don't dress like a tourist (bermudas, hawaiian shirts and baseball caps) cause not only you will be blank of all the laughters around, but youll be an easy target of the pickpockets! LOL.

and if you go out at night, go to Momma in Polanco and with a safe taxi, those aoutside the hotels. Youll love this city, for their people, food and historic relevance.