*Except for the school requirements, I would recommend you check out Fernandina Beach/Amelia Island. It has pretty much everything you listed... except good schools.
JIA (Jax Int'l Airpt) is on the north side of Jacksonville, so an easy drive from Fernandina. It isn't a horrible drive from most areas of Jax, unless you are going at rush hour traffic time. I lived on the South Side for many years... from Mandarin (southside suburb) it is about 30-40 minutes to the airport depending on traffic. Westside... probably about the same, but then you are on the other side of the river from your beach destination. That means a good 45 minutes to go to the beach.
St. Augustine my be worth looking into. I have heard that some of St. John's County's schools are good.. but I haven't lived in that county, so have no first hand information. And you add another 30 minutes to a trip to the airport. (which I only mention, b/c I'm thinking your husband is going to be doing a lot of traveling, right?)
There are several magnet schools in Jacksonville, so I'd be leery a bit of some of the others. I know that they are highly sought after and competitive to get into. It's been many years since I lived there and the schools that used to be the "good" schools, probably aren't anymore, since there are schools now that didn't exist then. Personally, if we were to move back, we would likely look somewhere along the west side of the intercoastal or in the Mandarin or old San Jose areas. But that would all depend upon the commute. My husband's work commute wouldn't be fun from those areas...
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Deerwood is on the southside, sort of between the St. John's Town Center shopping development (near the University of North Florida) and Mandarin. San Jose is a bit north of these areas, closer to the river and downtown.
Deerwood, 20 years ago, was a high end area of town. Deerwood Country Club, St. Johns Country Day School, etc etc.
It's about 10 minutes northeast of the Mandarin area.
The shooting of the black kids in the car by the 40something year old man over loud music at a gas station a while back (that the trial has been in the news recently) happened at the gas station at a main intersection right there at Baymeadows Road.