I recommend this place, but read on as there may be things you don't like.
PROS: This is within walking distance of many of Mexico City's top attractions, and the Alameda (a beautiful park) is only a couple of blocks away. The price I paid ($30USD/night) was amazing for a place that can sleep up to 6 people. I wish I had brought some friends with me! Marcye is also a great host. Check-in and check-out was very easy and she replied to all of my questions very quickly, both before and during my stay. If you don't like this particular place, I would still suggest looking at her other properties.
CONS: The street this building is on is not very nice. It seems perfectly safe, but there are homeless people sleeping outside. (If you've ever lived in a big city, you know that this doesn't mean it's a bad neighborhood. But if it's important to you, you should know this before going. Also, if you plan to do most of your sightseeing around the Zocalo, you may prefer to stay closer.
I would stay here again, especially if I came with other people and could split the cost.