We were in Mexico City that week about ten years ago. We hadn't realized that the big gift-giving day in Mexico is Three Kings Day, January 6, so we were surprised at the crowds shopping in the central city. I think some of the streets were closed to traffic. But the festive atmosphere added to our enjoyment, and we had no trouble seeing the usual sights.
We weren't there on New Year's Eve, but I'm sure there were celebrations, and probably fireworks (any reason will do for fireworks in Mexico). The tradition is for families to stay up till midnight and then eat grapes, a symbol of good fortune to come in the year ahead.
This will be a great time for your visit to Mexico City as long as you don't expect tranquility!