How far away are you willing to live? MacDill is about 15-20 miles from where I am by USF. How soon are you moving to the area? Personally, I'd look into townhouses (kid I work with is an Air Force Reservist and bought a townhouse in Clearwater for $65k and is paying less per month for mortage, insurance, and maitenece fees than for a comperable 2 bedroom apartment).
Place to look for apartments: Carlton Arms Apartments.