There are several good campgrounds right in Daytona Beach, subject to the caution that they jack up their rates sky high when there are major events going on at the speedway.
One that we rather like and have stayed at more than once is the Clark Family Campground near Orange City. Clark Family Campground - Home
It's economical, nice, and a down-home-friendly sort of place. Our favorite spot is a pull-through space next to the goat pasture. The goats are quiet neighbors and, surprisingly, get along fine with our three dogs.