This is a tough one. There are many nice places near that school but they are zoned for Lely high which does not have a good reputation.
http://www.city-data.com/forum/flori...ol-naples.html
I would look at in the Gulf Coast zone, which is mostly North Naples or Palmetto Ridge, which is mostly Golden Gate Estates. Both will be terrible commutes for you, especially in the winter.
There are plenty of decent places to live in Naples. There are a few bad pockets (Naples Manor is one of them) and they are easy to avoid.
Good luck on your new job. What will you be doing at Parkside?