Here are three different accommodations within a 10-minute walk to the Zocalo (central plaza). We have contacted the owners for special rates just for you.
1. El Arrayan — 2 small furnished apartments:
$48 USD/night without discount.
$1,082 USD/month: $18,256 MN, Minus 20% = Our special discounted price: $14,600 MN

2. Meson Amanda—Small private rooms with private bathroom, shared kitchen in the courtyard.
Our special discounted price: $5,000 MXN per month

https://www.airbnb.mx/rooms/28657256source_impression_id=p3_1727470858_P3YhL4VZMGVnuIR
https://www.facebook.com/tepozmesonamanda
3. Immersion: live with a local family. Rooms on 2nd floor, 1 with 2 beds, others with queen. All have views. Shared bathroom. Includes full Mexican breakfast.
$6,000 MXN/person/month