Trip to city centre from Sevilla's airport:
The easiest thing is to take the "EA-Especial Aeropuerto-Prado" bus that departs from the airport and after 6 stops, leaves you at Prado de San Sebastián Station (30 minutes, 4€). From here you can walk to the hotel (10-15 minutes to the area where the Cathedral is located) or take a taxi (5 minutes, 4€).
If you prefer, you can take a taxi directly from the airport to your hotel (15 minutes, 22€).