Mexico City is a world class city. It's big and busy just the way I like cities.
Take some time to travel around to the various neighborhoods. Condesa, Roma and Coyoacan are some of the best. There's one neighborhood called Zona Rosa. I don't care for it.....the shops, restaurants and clubs are flashy and cheezy, just like the people who go there.
The metro is cheap, clean and fast. Taxis aren't expensive.
Google Mexico City and you will discover fantastic museums, art galleries, shops, pastry shops, etc.
There are a few areas in Mexico City that have a concentration of informal taco restaurants (they serve more than tacos). These spots are where people of all ages and social status come to grab a bite to eat after a long night of partying. Lots of fun.
Have fun. Keep your wallet safe. The people are fun and educated. On Sundays, one of the major roadways, Reforma, is closed to traffic and is perfect for bike riding and strolling.
The men ( and women) are sexy. Unlike the States, where hooking up with a guy often becomes a robotic soulless experience, generally speaking, Mexicans are warm, kind and respectful. Don't forget your manners.
Go to the big Sunday flea market.
Visit the state run arts and crafts stores. High quality stuff.