My husband and I had a wonderful time staying at Alba's apartment with our four month old daughter last week. We enjoyed the location - the neighborhood is cool and diverse with lots of great bars and restaurants. Definitely head to the pedestrian street Blai for tapas and pinchos! It's a bit of walk to the main sights, but Barcelona is a beautiful city for walking and the Metro is very close and easy to use if you prefer it.
The front terrace off the living room is so lovely. The view isn't particularly spectacular (it's only on the second floor), but it is a very nice spot to enjoy the weather while having a cup of coffee or a glass of cava.
The one thing that would have made our stay a little nicer is if the apartment had been more generously stocked with basics. There were just two rolls of toilet paper, no paper towels, just one wine glass, and only two bath towels for two adults. There was no laundry detergent - I don't necessarily expect this and always bring travel-sized Tide packets, but I do think it is a nice touch when the host offers it to go along with the washer.
Now, a few notes for anyone considering renting this apartment with kids:
* The apartment is on the second floor, but there is a tiny (comically small, actually) elevator that will fit a small umbrella stroller.
* When the travel crib was broken, Maria generously provided us with the bedside bassinet that her baby had outgrown. The bedroom is dark, quiet, and separated from the kitchen/living room by two doors, so it worked out very well for us to put the baby down to sleep while we had wine and snacks on the terrace.
* There is a shower, but no bath - fine for us, because we're lazy and take our baby in the shower with us. :)
* The washing machine is a great amenity, but remember to bring detergent. Pro-tip: there is a rapid 30-minute cycle that you probably want to use if you're just doing a load of travel clothes before you head out for the day. Note that it is just a washer; as with many places in Europe, the expectation is that you will hang your laundry out to dry. Alba has a great drying rack and the side terrace by the bedroom gets tons of light during the day.