F6, F7, F8, E7 etc are very safe sectors of Islamabad. These are the most commercialized sectors and very civilized people live here. These are also the most expensive to live-in areas of Islamabad but their high prices pay off when you see how well maintained each area is. The roads are clean and you can walk alone even during the night. The houses and apartments are close together so people do socialize quite a lot.
Hope you find a nice place,
Good luck