We've been using Airbnb for a long time, but so far it's The Best Experience, period.
Maria is an awesome host, we felt like we were a part of family, no less. The apartment itself is ideal for living - it has everything you might think of, and even more. It's extremely cozy, clean and quiet, peaceful neighbourhood, a bunch of stores nearby, a gorgeous park, a few minutes to public transport..
Seriously, can't recommend it high enough: if you're searching for a quiet apartment in Valencia, distant enough from the noisy touristic city center, and this one is available - I don't believe you'll find something better.