The city offers tons of exciting experiences for the whole family! There is the Museum of Contemporary art down town, which offers hands on projects for kids, the Public library with an awesome interactive kids room, and the Jacksonville Zoo where you can get upclose with lots of different animals.
There are lots of parks all over the city, many with playgrounds. In the summer, take the kids to the beach for an inexpensive family fun day. If you are stationed in Mayport, the Little Talbot State park is a huge nature preserve with trails through the woods and along the beaches.