Have just returned from a weekend break at Miguel's apartment in the old part of the city. The apartment is very central to lots of sights in Carmen and surrounding areas with lots of cafes/restaurants within walking distance.
From the photos we thought the apartment was slightly bigger and brighter than advertised. We spent most of the day out sightseeing so it wasn't really an issue. There was a little bit of noise on the Saturday evening in the street outside and from the apartment above but it settled very quickly and it didn't disturb our girls sleeping.
We hired bikes for a full day and cycled along the Turia Gardens to L'Oceanogràfic which was a great day out. If you need a left luggage facility the bikeme company on Carrer dels Cavallers is great and will let you leave your luggage if you've hired bikes from them.
Will definitely return to Valencia as it's a beautiful city and our girls loved exploring round the streets and sightseeing.