To go to 11 cities in Pakistan in 14 days will be extremely hectic and is only feasible if you really really really want to see all of them in the shrotest possible time.
Pakistan is a country of extremely diverse cultures and landscapes. I am assuming you are visitng Pakistan as a tourist and just want to experience the rich culture and interesting sights. If you have another purpose (writing a book etc), you may have different priorities, so you can ignore parts of this post.
Pakistan has 3 big cities that most tourists go to. Karachi, Lahore and Islamabad/Rawalpindi. From a touristic standpoint, Peshawar and Quetta offer some unique cultural insights but they should be explored in due course. If you are a lover of natural beauty of mountains then Pakistan's northern areas are second to none. You should plan a trip to land in Islamabad, stay a night to get over the jet lag and then go on a one week trip to Naraan and Kaghan Valley. It will take you through some of the most breath-taking scenic routes you will ever seen. Once you get to Naraan (with full service hotels and a bustling market scene) you should spend 2 days there and explore Lake Saif-ul-Mulook.
Another favorite mountain spot is through Swat Valley. Again you can go from Islamabad and get to Saidu Shareef. From there the drive upto Kalaam is very scenic and you should stay there for atleast two days and enjoy the moutain hiking and exploring.
Gilgit is another mountainous region. While Naraan and Swat are green mountains, Gilgit is more like Yosemite (rock-like barren mountains). Western tourists flock to the area due to its breath-taking beauty.
For a luxurious experience of our hilly areas, take a 1.5 hour drive from Islamabad to the picturesque town of Bhurban. They have a great hotel there, with amazing views. You can then take day trips to places like Murree, Nathiagali and other assorted places around Murree. Its very touristy, is usually full of people and a lot of fun.
Lahore is considered the cultural capital of Pakistan, with many historic buildings. It was the capital of the whole Punjab province and thus boasts a immense Fort, the Badshahi Mosque, a vibrant inner city with a bustling bazaar scene and countless bargains. It has atleast 3 world class hotels. If you want to experience the cultural heritage of Punjab, then Lahore is a must-see.
Karachi is the biggest city in Pakistan, and being a coastal city it has beaches and an amazing variety in the shopping scene and world-class hotels. Its a very metropolitan city.
Islamabad is the capital city and is practically a bland bureacratic town. It is typically only used as a landing station as it serves as a gateway to our Northern areas and has some good hotels to stay in-between. Its twin city, Rawalpindi, has some some history and culture.
Peshawar and Quetta are much different from the other three big cities mentioned above. They have a unique culture of their own. If you are only going to Pakistan for 14-15 days, and are planning to cover a whole lot of our northern areas, then I wouldn't advise you to go to these two cities. Pakistan's northern areas are maintained pretty much in their natural pristine way, and one side-effect is that most roads are narrow and winding and thus travel can be quite tiring.
