I stayed at Daniella's place for 2 weeks while studying for some exams and I can't recommend it enough. It's a small apartment but the bedroom is large, bright and airy and I had everything I needed. Access to the bathroom is through Daniella's room and I felt awkward at first but she really was the most accommodating host and didn't show even a hint of annoyance! A word of advice for big-packers, leave your heavy bags behind unless you want to break your back lugging it up and down the 4th floor! I had no choice with the heavy bags as I was carrying a bunch of deadweight books with me - but I was mentally prepared to do some heavy lifting from the beginning.
Daniella herself is great- she lets you be, but is always available just in case you feel like a chat! Always responsive on phone and whatsapp, and helpful whenever you need advice.
The kitchen is functional and lets you do some light cooking if needed.
The area is awesome, and promises to give you the classic west village experience, with PLENTY of cafés, vintage stores, bars, restaurants, grocery stores, delis and when you're done with the eating and drinking, go for a Sunday morning run in the Washington square park a block away!
Many transport options - access to both the 1 train and A,B,C,D,E,F trains is very close by, and it's easy to hail a cab too.
All in all, a great first experience with airbnb!