ESL Teacher Looking for Room

hello! I am moving to Madrid from September 2024/Start of October-July 2025 to work at a school and looking for a room. My budget is $450 max with utilities included and am hoping to live in/near Atocha, Retiro, Adelfas, Lavapies, Pacifico. I have one cat but she is very docile and I will keep her in my room. I can also put down a pet deposit to cover her. I am 37, calm, and love art.