Better you come in your own car from Karachi, would save you a lot and will give you immense touring experiment.
Travel upto Gilgit via Babusar Top, travelling through Naran. Have stop over at Naran.
I would recommend go to Astore, to visit Skardu, while travelling in your own car. Stay at PTDC at Rama, enjoy Rama Meadows, and Rama Lake. While moving up to Rama, hire Jeep from Kamran Hotel, Astore, who shall pick you for crossing Deosai uptill Skardu. You will enjoy Chilam Chowki, Sheosar Lake, Bara Pani, Deosai meadows on the way. After reaching Skardue, visit Skardue tourist places in the same jeep and travel back via Deosai in the same jeep to Astore. You jeep will cost you 20 K for round trip plus charge for local visit at skardu.
If you want to continue, there are quite few more places in Astore like Ardang Nala, Rupal Valley. Each visit would cost you 5 to 6 K. If you have two more days on your disposal, and can take Army Permission, you can visit Minimarg and Domail with a night stay at Army Mess at Domail, a place which is way beyond beautuful than anyone's imagination. This Minimarg shall cost you 10 for Jeep plus 2 K for stay. On your return from Astore, you can opt for Fairy Meadows. Drop you car at at Raikot Bridge. Jeep would cost you 6.5 K for FM. Pony would cost you around 2.5 K till FM. Per night stay would be 4 K for entire family room. FM trip is a day affair. On exit, take your car and travel back via Naran.
Astore has much more to offer than Skardu and Hunza. Gilgit is highly not recommended being a hot place for stopover, plus it has no day trip in its surrounding to offer except Nalter. If at all you have to travel towards Gilgit, go directly to Hunza, for local sightseeing, and for travel uptill Khunjrab.
Don't rely hotels with big names, like PTDC except Rama. See the quality and negotiate the price.
Above plan would cost you 120-150 K for 10 days plan, excluding travel cost from and back to Karachi.