Before the rainy season (and before you have to cross knee deep water in Spiti) I suggest a tour from Rishikesh via Spiti valley to Jispa and onward to Leh. From Leh with inline permit (600 INR) the lakes are another possible target. Then back either via air (if time is a constraint) or Jammu/Kashmir (long and potentially dangerous) or just the quick reverse via Rohtang tunnel and Manali (the road from Mandi to Chandigarh is total shit and you have to overtake ca. 500 trucks uphill - bring a gas mask).