Karimabad makes a natural base for exploring the wider Hunza region. The roads up the valley are dramatic in every direction, so even a "day trip" can feel like a small expedition. Most travellers spend at least a couple of days pushing further up the Karakoram Highway into Gojal — Passu and the famous Cones, the Hussaini suspension bridge, Attabad Lake — and many continue to Sost or right up to the Khunjerab Pass on the Chinese border.
Closer in, the old village of Ganish and the trail up the Ultar gorge (above Karimabad) can both be done in a morning or afternoon. South of Hunza, Gilgit is the regional hub and a different feel altogether. The Battura Valley and the side glaciers reward longer walks if you have the time.
