If cozy translates for you as cramped and noisy, this won't be your cup of tea, but I found it to be cozy indeed and decorated with a pleasantly minimalist sensibility.
The stairs were a challenge for my old bones, hauling heavy film equipment up and down three flights twice a day and I did a bad thing: in the midst of transferring my gear in stages down to the first floor I had an unforgivable senior moment –– I exited the building having left Lilly's door open with the key in it. Her text to me hours later was stern, as it should have been, but still, she was gracious.
Lilly has a Slavic background with barely a trace of accent and is a good person whose profession as a psychologist is helping clients and mentoring students. She is no-nonsense straight ahead and answers all questions, but will not afflict you with frivolous small talk. The area has many of the New York hallmarks of quirky decaying infrastructure (the Tenement museum is blocks away), but is a current hub of gentrification as advertised with all the attendant cultural offerings of a 21st century polyglot city.