There are many public parking spaces in Granada but only one of them has reasonable prices for stays of longer than 24 hours. It costs 35 euros for one week.
There is more info on this page.
http://granadamap.com/so/index_en.htmThere is a page which has information about all the carparks with prices here.
This page shows the nearest parking places to Plaza Nueva.
http://granadainfo.com/car_parks1.php