The Karakoram Highway
Islamabad to Khunjerab, section by section, including the stretch several governments advise against travelling through at all.
The KKH climbs from the plains to the Chinese border at Khunjerab, and for a lot of people it's the reason they came to Pakistan in the first place. Ask how long it takes and you'll get a number that helps nobody. The sections are not alike, so take it a section at a time.
Islamabad to Mansehra
Motorway, then good road. Fast, forgettable, and reliably the part people leave out of their own estimates of the drive.
Mansehra to Chilas, via Besham and Dasu — read this section twice
This is the stretch carrying an advise-against-all-travel notice from several governments, and on the year-round route there is no way around it.
Two things follow. One is insurance: advisory-linked policies may not cover this leg, which is a separate question from whether you personally feel fine driving it. The other is that flying to Skardu or Gilgit removes it from your trip completely, and that's a reason to prefer the flight that has nothing to do with convenience.
In summer, Babusar bypasses much of it via Naran.
Chilas to Gilgit
Past the Nanga Parbat viewpoint, past the turn for Fairy Meadows at Raikot Bridge. This is where the landscape starts doing what you came for.
Gilgit to Hunza
Short, metalled, and the stretch you'll still be describing when you get home. Also landslide-prone, which is the one thing worth building slack around.
Hunza to Khunjerab
Through Gojal, past Attabad and Passu, up to the border. Whether the road is open and whether the border is open are two different questions on two different calendars. See passes and roads.