There are a couple of laundry places (laundromats) in Granada for example Tintorerías Niágara.
They charge 5.80 euros for a 6kg load.
General info: http://www.tintoreriasniagara.com/servicios.html
They have several branches in Granadahttp://www.tintoreriasniagara.com/tiendas.html
The laundry service in Hotels is very expensive.
Unless you have money to waste it may be a good idea to use alternative methods.
Many short term rental apartments have washing machines included in the price so
washing your clothes is free.
If you visit this page http://www.granadainfo.com/apartments.htm
Click on the washing machine box and you will only see places with washing machine.
Most places don't have clothes driers because it is so easy to dry the clothes in the sun.
Boabdil house has a Bosch washing machine with a 1000 rpm spin and you can hang your clothes up with views of the Alhambra.
More info here:http://granadainfo.com/bo