Looking for a cozy home for rent in Berlin

Hi! Me and my cat are looking for a cozy home for rent in Berlin, we are from Ukraine. I work freelance at home, in my spare time I go to courses and dancing: 
room up to 500€ or sublet apartment up to 700€
near the U-bahn/S-bahn 
starting in October-November
long term
possibility of registration

Please, any offers in private messages!