How you get to there can vary depending upon where you're headed there from. If Delhi, then the two best ways to get there are by air and by road. The latter is only an option in the summer/monsoon months when the Manali-Leh road is open.
Assuming you're headed there in the summer, taking the road has its advantages especially since Manali onwards starts an amazing roadtrip. The good thing about taking the flight is that you save on a lot of time... the Delhi-Leh flight is only an hour and a half.
Leh is the city which you can use as your base. From there, you can take NH1 in the direction of Kargil. This is a great bike ride... you pass by river confluences, the tourist-trap called Magnetic Hill, and you climb some very tall peaks on an Enfield... the range of landscape is truly astounding.The main place to stop here is an ancient place called Lumayuru... a 5 hour bike ride away. It's a Buddhist place atop a hill with a famous monastery. Kargil itself isn't interesting per se, though many people visit it out of symbolism.
The other place you must visit is the Nubra Valley, for which one has to get a permit. I went with a foreign student, so I assume PIOs will be okay. Here, too, there is a lot of landscape to pay attention to, starting from ride up to Khardung La from Leh. That road is widely claimed to be the "highest motorable road in the world". It can get pretty damn cold and the road can be problematic but of course the view around is a solid A. Depending upon the season you visit in, there might be decent amount of water in the rivers down in the valley, so the drive down and through it might even be colorful. In the colder months, one drives through a wide valley of barren rock. It is full of villages interspersed with Barracks and other security installments.
In the valley, you'll want to stop to eat at some point... probably Pullu for Maggi, momos and chai. There is an Army Dosa stall somewhere around Hunder which would still be hours away. Hunder is the place with the double-humped camels which you can ride. Otherwise, there is little to do hear except drink brandy and find peace overnight in a quiet guest house.
There are a couple of other villages one can stop by in to eat/stay overnight, but your main destination is the tiny village of Turtuk which is the last village one is allowed to visit. There was literally a bridge with a metal door and a lock in front of us. Our cab driver pointed in the direction of a mountain in the distance and told us, "That's where the Pakistanis are".
Turtuk is quite untouched by tourists. It is one of the most calming places to visit and the sky above is really something else at night. There is little to see here except how the Balti people live. We were told that an ancient tribe lived nearby in the mountains and claimed to be descended from Alexander's troops. There is a little, old monastery atop a hill. And, of course, is the natural beauty which you must google right away.
You can also go to Pangong Lake, though I couldn't fit it into my schedule. Leh+Lumyuru+Nubra Valley took me well over a week. So you'll have to keep that in mind, especially since you have to acclimatize once you reach Leh. Recommended modes of traveling around are by bike to Lumayuru and by shared cabs to Nubra Valley.
Sorry if this is too much info. I get excited about these things.