8 days are enough to explore Spiti by car from New Delhi, You can take this route: Delhi - Manali - Chandrataal - Kaza - Kibber - Dhankar and Hikkim and then return. You must keep a check on the weather, you might get rainfall till Manali in the monsoon season.
You must also keep in mind the altitude change that may cause severe headaches and nose bleeding to some, thus prepare before hand. Carry Diamox and take it before you start your journey from Manali. Alternatively, for better acclimatization you can choose the Shimla - Peo - Nako route. Go through the following articles for more details.
I believe you'll be starting from Delhi by car. Spend a day or two in Manali. Helps you acclimatise better. You should visit the Key and Tabo monasteries. Kaza and Kibber villages should also make an appearance in your itinerary. Also, I would recommend visiting the Chandratal lake too.