accomodation in downtown Reykjavik

Sabrina ,23 year,no smoking  .I'm looking for accomodation  with other students in Reykjavik downtown , but I all sorts of possibilities even on a different budget, I prefer contact mail.I am a basketball player and I would also like to look for an opportunity and continue in my passion. I come from an Italian region among the most beautiful places in the world and in my veins flows sicilian blood, I feel volcanic and Iceland is the most suitable place for me