If you don't want to live in Calloway, even though it is close to Tyndall not that far out of the way and well worth it is The Woods subdivision, The Woods III, Harrison Place (all off of Harrison Avenue and near Lynn Haven. In Lynn Haven is Mowat Highlands which is going to give you better elementary, middle and high schools.
My dad is retired Air Force and if you can't live on base these are your best choices. I would not, however live in a place where Jinks Middle School is zoned as I don't think that you would care for it. Mowat Middle School is a good school, Mosley High School, and Lynn Haven or Hiland Park Elementary schools are good. Tyndall Elementary is also a very good elementary school.