Lima: I would be shocked if you found something for $250 USD, unless you are out of downtown, a fair bit out and are truly not concerned with amenites. I don't think anyone with a website, email and a facility with English would be renting for that amount, since they have access to social media and the like. Local newspapers would be the place to look, perhaps the classifieds of El Imparcial, or Noticias - Voz e Imagen de Oaxaca. February is high season, as well, for snowbirds. You're asked to pay about 100 pesos a night, the amount the most modest hostel charges, and they are far from serene.
Alvin Starkman - Casa Machaya Oaxaca Bed & Breakfast