I agree with Maura, Mexico City is a dangerous city is not like some others in the world but you have to take precautions when you are there. Being mexican I have to say I hate being there by myself .. I alwasy ask my company to send a driver to pick me up at airport and drive me on the city.
But also I have to say if you have someone to tour you , Mexico City has a lot to offer, a lot of restaurants with all kind of food, bars, clubs, museums, and a lot of fun stuff to visit around like Cuernavaca, the pyramids, the beautiful lake at Valle de Bravo, Tequisquiapan, etc, etc..
So is fun and safe if you go with people that knows the city and take you to the right places.....