We just had a great trip to Naples last winter. There's the beaches, boat tours to see manatees, dolphins or Keewaydin Island, shopping and restaurants on 5th Ave as well as 3rd St. South (make reservations early, severals days in advance, especially for popular places like Tommy Bahamas restaurant which btw would be great with kids if you go early in the evening.) Those are nice areas to stroll, shop, and after dark enjoy the strings of lights in the trees and people watch.
You can visit the Everglades or do national park boat tours of the 10,000 Islands.
We took a very slow, gentle manatee tour out of Port of the Islands that didn't scare the wild manatees like the big tour boats do and would be good for little kids.
There's the Naples Zoo and Caribbean Gardens (which we did not do) The Children's Museum of Naples, a waterpark called Sun N' Fun Lagoon, Imaginarium Science Center, and several park nature centers around. The Naples Botanical Gardens has a LEGO exhibit.
I don't know if you plan to go to a hotel but the waterslide pool at the Waldorf Hotel is fun. You could, ah hem, sneak in there - drive up, tell the valet you are staying at their sister property the Edgewater Hotel, park in the underground lot and walk out to the pool. And there is a trolley that takes people to their beachfront through a mangrove lagoon.
Clam Pass Beach offers trolley ride to a beach with a snack bar and rentals.
http://www.naples-florida.com/beach.htm
It's beautiful there. I wish my parents would get a condo in the area!