नमस्कार
Well..there are lot many places near to leh... i hope you have searched on web and found some information about Nubra valley,Pangong,Tso Moriri,Kardungla...these three sites are popular ones...there is a lot to explore in that region..like one can go to Zankshar,Drass,Kargil...can move further north to Nubra valley...can explore Spiti,lasha valley....but it all depends how many days you have and what kind of travelling you looking for...
After Reaching Leh..you will have to hire SUVs for visiting all these places...please try to get inner line permit as soon as you reach there..