Dear Mohim,
You are going in Rush season, as 27 June or 28 June shall be Eid, so you are basically going on Eid holidays means, everything shall be fully loaded, hotels shall be expensive, roads shall be populated with vehicles, road blocks and traffic jam is normal, i would not suggest you to go during that days on your own vehicles but if you are really indeed interested in that time zone. Then do following. you can see some tour plans on this website
Start from Karachi 
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Day 01: Karachi to Multan in 10 Hours time , stay in Hotel One or Paradise Hotel
Day 02: Multan to Islamabad via National highay till Gojra, Gojra to Islmabad on Motorway, 10 Hours Driver stay in Rawalpindi in Royalton Hotel
Day 03: Rest Day in Islamabad, sightseeing Islamabad , move towards Murree only one drive stay in Arcadian Murree
Day 04: Visit Patriata Hills, Mall Road, stay in Hotel in Arcadian,
Day 05: Visit Nathiagali, Aybuia stay in Nathiagali, Hotel Elite or Green Retreat
Day 06: Move towards Abbotabad City, reach Kewai Water fall near Balakot, Park your vehicle in kewai Waterfall, move towards Shogran on Jeep, stay in Shogran Lalazar Hotel or Arcadian Sprucewood
Day 07: Visit Siri Paye meadows on Jeep , back to hotel in 4 to 5 hours and stay in Shogran
Day 08: move via jeep to driver your vehicle towards Kaghan, short stay kaghan, reach naran in 3 hours time stay in Naran PTDC, or any hotel, may be Greywalls Cottage or Trout Lodges
Day 09: Visit Lake Saiful Malook on Jeep, Jeeps take near 5000 during Eid Season for 3 to 4 hours Trip back to Naran in eveing
Day 10: Move from Naran early morning towards Babusar Top, you can reach in 2 hours, while short stay at Lulusar Lake which is 10 km before babusar Top, , Babusar top is 13700 feet high so cover yourself with clothes and your kids, then don't wast much time there, as you will go towards Chilas and eventualy after 7 hours you reach Gilgit stay in Gilgit PTDC
Day 11: Visit Naltar Valley , get Private Jeep Booked from Gilgit City, takes near 10,000 or more , visit till Naltar Lake, back to Hotel in evening
Day 12: Move from Gilgit to Hunza in 2 hours time, short stay at Rakaposhi View Point, the reah hunza, Visit Baltit Fort and check into Hotel, ( Serena hunza, / Hunza Embassy Hotel ) or Hunza View Hotel
Day 13: Move towards China border via Attabad Lake Tunnel, full day Excursions
Day 14: Rest Day in Hunza
Day 15: Hunza to Naran Valley via Chlas Babusar Top Road and stay in Naran
Day 16: Naran to Islamabad in 9 hours and stay in Rawalpindi
Day 17: move towards Multan
Day 18: Multan to Karachi for end of tour.
If you need any more help you can call me anytime, or like my page on facebook for northern areas updates.
0312 5120 590
