Congratulations on your new arrival!!!
If you're looking for Military Campgrounds within 2 - 3 hours of Daytona, you have Mayport up by Jacksonville, and King's Bay in Georgia. There are some others, but these are the only 2 I've been to and they're both nice. Check out the Facility Listings under the Recreation Facility Info tab up at the top of the page.
There's also some really nice Florida State Parks within that time frame. Two that I can recommend are Stephen Foster Cultural Center in White Springs and Myakka State Park down near Sarasota. Both are water and electric hookups only, but there's a dump station in each.
You're also only a couple of hours from Ocala, another nice area. Silver Springs is a great area with lots to do on a weekend.
Of course, you're right up the road from Mouseville, but I wouldn't wish that on my worst enemy.
Whatever you decide, drive safely and have some great trips!!