Not burgers, but I was going through my phone pictures the other day and came across the dinners from Coz- gahhhhhh such great food!
Do not see it mentioned often on here, but a small place right around the corner from Casa Mexicana (between CM and 3P's) Colores y Sabores was very, very good. They served a green crema with the chips and it was incredible. I went there 3x on my last trip- it was just too easy and delicious.
Very convenient, cheap and easy if you are staying at CM or any of the other hotels right there.