If you haven't been to the Canaveral National Seashore you should add it to your to-do list. It's a wonderful place to visit. You will find nature trails, beauty, and history all in one place. My kids love this place. My son especially loves the trails on Turtle Mound, which puts you in a breezy area overlooking water and you have a great view.
Turtle Mound is an historic midden (a shell mound from the native Americans). It's huge and they have built a wooden boardwalk trail that goes over it. So you wind your way on the trail to the top of the midden. Along the way you see a lot of nature and once you get there you have a wonderful view of the area. At the bottom of Turtle Mound there is a trail that leads along the water back to the other side of the midden. Both trails are short enough for kids. The boardwalk one is wheelchair and stroller accessible, but the one along the water is not. But don't let that stop you from going. Even if you can only do the one boardwalk one on the midden it is well worth the trip!
There are also other short hiking trails in Canaveral National Seashore. Most are around a half a mile or less. There is also a visitor's center, covered picnic tables near the visitor center, kayak/canoe launch areas, beach access (undeveloped beach!), public bathrooms, and an historic house you can tour.
This is a great place to visit! You can find more info here.
Here are some pictures from Canaveral National Seashore: