The closest airports are in Rome (Fiumicino Airport https://www.adr.it/fiumicino & Ciampino Airport https://www.adr.it/ciampino ) and in Pescara (Aeroporto d’Abruzzo http://www.abruzzoairport.com/). From Ciampino and Fiumicino there is a direct bus to l’Aquila (you can see timetable and fares here http://www.gasparionline.it/ ), which will leave you in Hotel Amiternum. From there take any bus going towards the city centre and get off at Terminalbus Collemaggio. GSSI is 5/10 mins walking from Terminal bus.
L’Aquila railway station is not well connected, therefore by train you should better arrive to Rome or to Giulianova (for those traveling on the East coast along the Adriatic sea). From there (Roma Tiburtina or Giulianova railway station) there are ARPAhttp://www.arpaonline.it/arpaonline/en/ buses leading to L’Aquila, which will arrive at Terminal bus Collemaggio. GSSI is 5/10 mins walking from Terminal bus.