Why pay upwards of €46 for a return taxi journey from Seville airport to the centre when you can pay about €35 to rent a small car for the weekend or €60 - €70 for a week?
On top of that you can then drive down to the coast near Cadiz, or Conil and enjoy a few lazy days by the beach.
Hispacar has consistently been the cheapest rental broker I can find.
Once you have booked you will pick the car up from Crown Aguila Car Rental at the airport. The usual policy is that you get a full tank of fuel and return it empty. However, if you are only renting for a short time and won't do the distance, explain this and you can usually return it full again.