Jacksonvillite here!
No, not much to do here in Jacksonville in the tourist department. St. Augustine is fabulous, tho. Beautiful B&Bs, as well as regular hotels, fantastic food and some pretty interesting sights, too. There's the oldest church in the country, as well as the "pool room" from It's a Wonderful Life...you know the scene I'm talking about, the one where everyone fell in the pool. Evidently, a lot of filming was done here on the First Coast during that time.
If you're ansy to get to Orlando, scrap taking A1A. Way, way long route. Just get back to I-95. My hubby and I make it from our front door to hopping on a tram at WDW in two hours w/out stopping -- add 10 minutes if we need to stop and use a restroom. St. Augustine is half-an-hour south of us, so it would be even less time for your family. Keep in mind the traffic on I-4 in Orlando is brutal during rush hour, so plan it so that you're not in it. We generally leave our house at 7:30 a.m. and are parking at MK at 9:30 a.m.
Please feel free to pm me if I can be of help if you decide to stay overnight in Jax and I can steer you towards some good eats/hotels.