You might check out the bay side area north of the new hospital. Lots of newer construction going in there, and generally not as pricey as being on 30-A proper. Yeah, it's mostly tract houses, but Adams Homes has a reputation for building reasonably well, and since it's new construction, they're built under a tougher code standard than something from the 70s.
One thing to keep in mind is that houses in non-rental neighborhoods don't appreciate as fast as rentals, but at the same time non-rental houses are less expensive.
One place to look is SeaBreeze which is in Camp Creek. It is non-rental and relatively reasonably priced. It is within walking distance to the beach and very quiet. There aren't a ton of kids because most homeowners are retired, but the general area from Camp Creek Lake to Inlet Beach is pretty much like one big neighborhood and there are many kids in this area. Flamingo Village next to Butler is another place to look. Grove by The Sea in Seagrove has some nices houses. It is rental, but there are several full-time families there and it is close to the beach. There are a lot of kids in Point Washington and that area is close to Bay Elementary school and not too far from the ball fields.
Since all the full-timers are spread out, we make friends through school and church more than in our neighborhoods.
The hospital area ones are Driftwood, and I think Mack Bayou something-or-other. Today would actually be a good time to be driving around since you'd get an idea of which areas might have drainage issues.