First time visit to Mexico City

I've done some basic research, bought a guide book, read travel blogs. Still this will be a first time visit to a massive metropolis. If anyone is willing to share, I'm looking for advice.

What should I know re transportation? Does anyone have advice for reasonably priced delicious food? I've heard Oaxacan cuisine is good. I'll be traveling with a pescatarian. I know we're going to the Anthropology Museum and setting up a tour to the floating farms. That still leaves a couple of days. What are your don't miss experiences? What have you really enjoyed? Are there good websites for finding concert tickets? What about safety?