Day 0–1: Start from Delhi at very late night and reach Shimla at early morning. Take a break for a couple of hours and leave for Narkanda or Rampur as long as your health permits. Otherwise, you may start early in the evening from Delhi and stay at scenic Sarahan. Then your day-1 won’t be a waste. Day 2: Leave as early as possible for Reckoning-Peo. From Wangtoo to Reckong-Peo the roads are very bad. Take some rest at Peo and leave for Nako. Nako is part of Kinnaur (not Spiti) but I hope one should include it in Spiti trip. Tented arrangements near Nako lake are nice. Day 3: After breakfast, leave for Tabo. Now the real Spiti begins via hairpin roads and barren valleys. You might face AMS here. So take necessary precaution. Tabo has many things to explore, including a monastery, its paints, Gomphas, and the silence. If possible carry tents with you and stay near Gophers in your own tent. Day 4: Leave for Dhankar. Unless it is moonlit night, staying at Dhankar is not so useful. During full-moon Dhankar is perhaps the most beautiful place I have ever been to. If you are staying at Dhankar, you can’t stay at Komic, (probably) (one of) the highest village(s) of India. If you ain’t staying at Dhankar, leave for Komic and stay there for the night. There is a thrilling bypass from Dhankar to Komic. Day 5: From Komic or Dhankar leave for Kaza. Then visit nearby Kee Monastery etc. No point of staying at Kaza, IMO. Leave for Losar and stay there. Day 6: Leave for Chandratal and spend the night there. If you are tired, skip Chandratal and spend more time on the villages of Spiti. Day 7: Leave for Manali and then Delhi. Well, in 7 days, exploring Spiti is very difficult. Also just exploring Spiti is a bit odd. One should include visiting Kalpa, Sangla, Chitkul etc on the trip as well. Else using the Shimla route is wastage of fuel. Good Luck!!
Happy Travelling!!!