Here is a link to the Department of Education site for Duval County. I find this report easy to read below are the schools in the area.
The Intracoastal West schools are: Brookview, Alimaconi, Chets Creek, Abess park, Landmark, Kernan and Sandlewood
The Mandarin Schools are: Greenland Pines, Loretto, Crown Point, Mandarin Middle, Mandarin High
Someonw mentioned Ponte Vedra. The schools are excellent but the average home prices in that area is much higher than Intracoastal West and Mandarin.
Another good school district is St. Johns County. Housing prices slightly higher than Intracoastal West & Mandarin. Schools to in North West St. Johns County are: Julington Creek, Durbin, Cunningham Creek, Fruit Cove, Switzerland point, Bartram & Nease There are some others but these are for the area Around Julington Creek, Fruit Cove and the Roberts Road area.
I hope this info helps you with school research