You did not mention how old your kids are, but our kids got bored with St. Augustine pretty quick. Now when we visit, the kids stay at home. It's a city rich with history, but not all that entertaining for kids. If your kids like Forts, then visit the Castillo de San Marcos. If they like animals, don't miss the Alligator Farm. You can probably keep them entertained for 1 day in downtown St. Augustine. There is also the St. Augustine Lighthouse and Maritime Museum. We go for a few hours on the free national park day. The view from the top is incredible. On a clear day you can see north all the way to Jacksonville.
We live about 90 miles north of St. Augustine and our kids go in the Ocean year 'round. For the locals, anything below 80 degrees is too cold to swim in. Our kids swim even when it is in the 60s (everyone thinks we are tourists). Being from Ohio, your kids will probably be fine with the Ocean water temps in January. We like North Beaching Campground. It is directly across from the beach on A1A in St. Augustine Beach. You can walk to the beach from your site.
There is lots to do in Jacksonville, which is a short drive from St. Augustine. Cape Canaveral and Space Center are not a far drive either. If you are a Golfer, be sure to check out Ponte Vedra just north of St. Augustine.
-Michael
