This 2nd story/ 3rd floor modern apartment with a full kitchen, lift/elevator, dishwasher and washing machine is a gem! They are perfect hosts and their friend Norma who oriented us when we checked in was very helpful. Located in a quieter neighborhood outside the historic center, it is very accessible by short hops on public transportation. If that is your preference, use a T-10 pass; multiple people can use the same pass and it gets you onto all public trans, including the Funicular that goes to the base of Montjuic. You need to purchase the Montjuic cable car ticket and I recommend a return ticket if you are out of shape as it is relatively steep.
Other notes on transportation: avoid Uber here, they cancel without warning. Taxis are everywhere and are relatively inexpensive in comparison to US fares. This city is fairly flat and highly walkable for most. Walking in the vicinity of Parc Guell and Montjuic is rather steep. Cars, buses, and mopeds fastidiously obey the traffic signs, although bicyclists ride on the sidewalk and crosswalks when there are not bike lanes.
If you are going to need more sleeping space than the double bed in the bedroom and the futon in the living room, there is a double in the loft that is accessible by steep steps and no railing, which can be kind of hairy, especially in the dark. There is one AC unit in the living room and a fan in the bedroom.
We stayed four days/five days in the late summer and found the 3 day Barcelona Pass to be almost completely useless. We only managed to use it for Casa Batllo and the Perdera aka Casa Mila. Parc Guell is not included. The Busturistic was disappointing and if you do use it, make sure to bring the piece of paper that looks like a receipt; especially if you get the Barcelona pass. It is a separate company and they will not let you on without it.
Alex and Gemma provide links after you book their apartment to purchase tickets to attractions that fill up in advance, including the above plus the Gaudi church Sagrada Familia, which is about 2 blocks away from the apartment. Every one of their suggestions was a must see.
There are an assortment of restaurants and cafes for every budget within walking distance. Our favorites were the modest Lucus Cafe and the splurge (for us) was 9 Nine. Both are great values. There are plenty of good vegetarian restaurants. Our favorites were Hummus Barcelona (great 4 item lunch including a not to miss tofu cream with rose jelly and nuts) and Biocenter, a true oasis of calm in the bustling center.
We highly recommend staying at Alex and Gemma's Airbnb and would not hesitate to return.