From Barcelona airport you could take the RENFE train (line C1) at the "Aeroport" station and get off at "Plaça Catalunya" (4 stops). Then, take the red metro line (L1) at "Plaça Catalunya" subway station and get off at "Urquinaona"(just next stop). In this stop you should transfer to the yellow metro line (L4) and get off at "Jaume I" (also next stop).
From Girona airport the bus service to Barcelona “Estació del Nord” is called Sagales. From Reus airport yo have the Igualadina bus service to Barcelona “Estació del Nord”. From there have a nice walk to the apartment with the help of the map we provide you.
For more info about metro, bus, airport transfers, prices and maps have a look to our Barcelona tourist guide.