22 years old girl looking for accommodation not too far from Manhattan and a nice roommate!

I'm a French student coming to NYC for an internship, and I'm looking for a place to stay (30min maximum from Time Square in public transports). I'm not too picky but I just want a private room and a clean house. I'm also looking for a roommate who would be part of this incredible experience I'm about to live. I will be staying four months (until the 25th of September). I love having people around me and even though I'm a bit reserved I like good talks and good laughs! I like to have some moments alone on weeknight (because I love listening to music and I will also have an essay to write). I love food (well I'm French) but I don't cook a lot. I like to workout and go for a walk on weekends, and if you want to come with me you are so welcome! I also love pets and I wouldn't mind at all if you have one. I'm looking for a roommate I would get along with and who would love to go out at times with me. I want to explore the city and learn as many things as possible!