My boyfriend and I enjoyed our stay at Julio's place. It's modern and trendy, a really lovely loft space that had all the basics we needed (and the small pastries and cava were a nice touch!). Do note that it is a three storey walk-up (the top floor), so it might a challenge for those with mobility issues or heavy luggage. The main space is air conditioned, though only fans in the bedrooms, so I imagine it can be a bit warm in the summer months (it wasn't too bad at the end of September).
The neighbourhood isn't quite downtown, about a 25-30 minute walk to the heart of the old city. Although we didn't end up exploring it too much, Russafa is a neat little neighbourhood; on another visit, we would spend more time there. It's also about a 5-10 minute walk to the Turia, at the Gulliver playground. Not too far from there to the City of Arts and Sciences, which is definitely worth checking out.
A friend of the host met us at the apartment and let us in; she showed us around and gave us a binder of recommendations for Valencia - very helpful. We would certainly recommend staying at Julio's, and would again!