If you want to see the real historic Pakistan, then I suggest you visit Lahore.
Islamabad is a very new city that is well-planned, the city does not have much of a rich history like Lahore. However, 32 km (20 mi) northwest of Islamabad is a very ancient city called Taxila. It is was an important city during Alexander The Great's campaign in South Asia and contains buildings and buddhist stupas from thousands of years ago.
I've spend much time in Islamabad and Lahore, and I would suggest you go to Lahore and go to a restaurant called Coco's Den after 8pm. Ask the waiter for a seat on the most upper level of the restaurant and you'll see a magnificiant view of the historic Badshahi Mosque lit up at night, theres nothing like it in the world. And in the morning/afternoon visit the Lahore Fort, which is next to the Badshahi Mosque. And then in late afternon you should viist the famous Wagah Border (Pakistan-India International Border). The Pakistani Rangers and the Indian Rangers put up an entertaining show. You can cross the Wagah Border into India if you have proper documents (Valid Passport and a Valid Indian Visa). For transportation, I suggest you take a rikshaw for transportation in South Asia, its cheaper and safer mode of transportation in South Asia.
I dont know much about Karachi. Ask PDF members who are from Karachi (most Pakistani PDF members here are from Karachi). I heard from relatives that Karachi is also worth visiting.
Finally, if you get sick of South Asia and the subcontinent all together then visit Islamabad, its the Europe of South Asia and you will feel much in home (less traffic, less pollution, less people, modern buildings, taxis (no rickshawas), greenery all around you, all the European/American cuisine you can think of).