Welcome to Pakwheels!
May I ask from where are you flying in?
Anyways, here is my humble suggestion - while expert guidance is expected soon.
If you want to visit Naran/Kaghan (specially on public transport), may I suggest you contact PTDC (phone: 0092-51-9272013, 9272004-08). Their direct bus service to Naran will start on 01 June 2015 (so if possible, book in advance). One-way fare is about 1650/person. The bus departs from Flashman Hotel, The Mall, Rawalpindi.
Spend a couple of days in Naran, and one day in Shogran. One day in Islamabad (no offence, but Abbottabad is not worth spending two nights - unless of course you have some plans there).
Then on your way back (if you really really want), visit Murree for a day trip from Islamabad. Be aware that it will be crazy crowded (with children summer vacation and just a couple of weeks before Ramazan).
Good luck and all the best for your trip planning 