We had a really good time in Anna's appartment. It was friendly, clean and well equipped (including a crib and high chair for our little one).

The area is quiet, not tourist crowded and unexpectedly hilly (so a baby buggy not really makes sense, ours stayed at the apartement most of the time).
Supermarkets, bread shops and fruterias are close by and many are open even on sunday.

For travelling familys: There is a nice playground and a shallow pool (open for swimming only in summer) in walking distance on the other side of El Coll park.

The subway station was close by with an easy transfer to the center. Yes, you need some time to get there, but our kids loved riding all the escalators and moving walkways in the metro stations.

Anna organized a fast and cheap (plus super friendly and highly entertaining too) transport from and to the airport. Thanks to Pablo.