Islamabad is the capital of Pakistan
A previous ti. Honestly it's Pakistan, and you can hitchhike inside the city if you are a foreigner. People will pick you up. They are curious about foreigners, and once you start explaining many of them will probably drop you off exactly where you need to be.
Go to the street called "Kashmir Highway" and go south on it until you get to the Great Trunk Road (N5), on which you go into the direction of Taxila. Just before Taxila you turn off to the right though, into the direction of Haripur. From there it is not far to Abbottabad.
If you want to take a shared taxi out of the city, take it to Taxila, and hitchhike from there.