Hi S.. I lived in Jacksonville all my life until I moved to Tampa about 11 years ago. Jacksonville has grown and changed so much in that time, but my parents still live in the area so I still know good/bad areas. One of the good areas to live is San Marco (a lot of older beautiful homes -- comparable to S. Tampa) which is close to downtown, but not too close if you know what I mean. Avondale is another good area and convenient to downtown and other areas. Ortega also has some beautiful neighborhoods. Steer clear of the Arlington and Ft. Caroline areas. They used to be fabulous areas to live, but are no longer good areas. Another area that is very nice is the area around World Golf Village. My parents actually live in World Golf Village and that area is really booming. It is actually in St. John's county, but just over the line. They have a nice school right down the street from WGV. There are also a bunch of other new neighborhoods being developed in that same area.
As far as schools go, I'm sure there are some good public schools in the areas I mentioned, but if you are looking to do private school Bolles has always been known as the premier. It is right on the river and close to San Marco. It's a beautiful campus! There are some other private schools in that area that are good -- San Jose Episcopal comes to mind. I know that Assumption, Bishop Kenny, and Episcopal were all good private schools when I lived there, but I don't know if they are still good.
As far as things to do...there's the beach. In my opinion, the beach is not as pretty there, but to a child I'm sure it's all the same. There is a children's museum near San Marco also. It's been years since I've been there, but I always had a great time there as a kid. There are many parks, malls, etc. as well.
Well, I hope this info helps you a bit. If you have any other questions, you can email me at ____@____.com luck!
K.