I would not recommend Jacksonville to anybody. I've lived here 4 years and it is a cultural void, as I've mentioned in other posts! As the main source of income is the Military Base, all entertainment / life is directed towards that (Strip Clubs, Tattoo Parlors, Chain Restaurants and Fast Food). I would not live here were it not for my husband being in the Marine Corps. We can't wait to leave!
Additionally, most areas of Jacksonville are a 45 minute + commute to the beach, and we don't get the benefit of sea breezes.
Wilmington would definitely be a better option. Statistically speaking the crime rate is quite high, but I've never personally had a problem down there. Wilmington has some degree of culture / life (a lot more so than Jacksonville) and is more aesthetically pleasing. It's got more shopping options, and some more interesting dining choices. Although parts of Wilmington too aren't right near the ocean, I still believe that it's a far nicer choice than Jacksonville.
I have had friends live near downtown however, and although the downtown district is going through a renaissance of sorts, certain areas still aren't all that safe and my friends have had problems with break ins/ auto thefts etc.
goldenage is correct that budget cuts have been made to our education budget as well. I have three friends here who are teachers who have all been affected in some way.
Wherever you choose to move, make sure you secure a job before moving
Although I'm sure you knew that already!
The best option may be to flood multiple regions with applications / your CV and see where the best offer comes up.
Let a city find you... and you might be pleasantly surprised