20 year old student looking for an accommodation for a 4 month internship in Hamburg City Center

Hi, I am a 20 year old student looking for an accommodation preferably near the city center of Hamburg. I am starting a hospitality internship and am looking for a place at the start of August till the end of November. I am a clean and sociable person and am very open to exploring the city. I speak German too and would love to practice speaking it some more. My budget is max. 500 euros/m warm. Please let me know if you have a room available xx