If you happen to come to Srinagar in Jammu & Kashmir, India, think about going for a hike in the Northern part of this mountainous state. One of the best places to start with would be the village of Naranag which is about 1.5 hours drive from Srinagar. One can hire a $40 sumo jeep or take two $3 local buses from Srinagar to Naranag. The beauty of Naranag is that, despite its numerous visitors - maybe, 30 people/week during peak summer days - the environment and treks stay pristine, the locals are welcoming and showing the true Kashmiri hospitality.
I was attempting to make a spontaneous ascent of Harmukh (5142m) near the first camp but stopped at around 4400m due to bad weather (at 3pm) and somewhat lose rocks. However, if one starts early in the morning (4am-5am) and is cautious enough on the rocks, the climbing may be very enjoyable and challenging. The top of the mountain (4900m-5142m) is covered by the glacier. Harmukh is the mountain from which K2 was discovered. Arguably, one can see the Rupal Face of Nanga Parbat at a distance of 100 km from the top of Harmukh.
Besides climbing, there are several scenic lakes around (Nundkol and Gangabal) that may put you into a meditative state if you choose to stay there for a couple hours. The lakes are relatively warm in late July (7C-10C), so one can go for a refreshing swim in their waters. There is also a several-days trek from Naranag to Gangabal Lake to Sonamarg through the mountain valleys.
As for the local trekking operators, I would recommend Mr. Mohad Aslam Kasanan whose family owns a guest house in Naranag as well as a summer camp/tent in the first camp (+919697560626 or +919858339208). Had very positive experience with those guys. Learnt Urdu a bit :)