1) Kaza. You can get to Kaza by road from Manali, it takes 10 hours and there are many Sumos that run everyday in the summer, along with a government bus. This route opens in May, until late september or October. During theothermonths, you can access Kaza from Shimla via Reckong Peo. The other places in Spiti can be visited with Kaza as your base.
2) Kibber, Key. Key monastery is one of the most popular locations here, and can be reached by a bus (30 minutes) or by cycling from Kaza. Alternatively, you can visit with Kibber and Key together. Take an evening bus to Kibber and spend the night there. walk down from there to Key early in the morning, have breakfast in the monastery and catch the same bus back to Kaza at 9:30 am.
3) Langhza, Komic and Hikkim. All these three places are close to each other, and do not have any buses plying between them and Kaza. Many people trek, while some hire taxis. Although, I must warn you that trekking at this altitude is quite taxing physically. Langhza is a village that is known for its pottery, and has a large statue of Buddha overlooking the village. Comic id the highest village in Spiti, and claimed to be the highest village in Asia. The post office in Hikkim is the highest in the world, and you can send postcards from here to anywhere in the world for a small price. Quite a fancy kind of souvenir!
4) Lhalung - Not too well known in the traveller diaries, this is a stunningly beautiful village that can be reached from Kaza by bus.
5) Demul - Another village that is a must visit.
6) Mudh and Sagnam - Mudh marks the beginning of Pin valley, and has a starkly different landscape as compared to rest of Spiti - much more green. Saginaw is another village just before it. both can be reached easily from a bus that leaves Kaza in the evening.
7) Dhankar - The old capital of Spiti, popular for its gompas and the Dhankar lake. One can trek along a tricky, steps path of 2 kms or along an 8km long paved road. Buses do not go up here.
8) Tabo - The thousand year old monastery, along with the caves make this a popular sight-seeing location for travellers. It is on the way to Shimla, 2 hours from Kaza. One can proceed from here to Shimla, or get back to Kaza
9) Chandratal - An absolute must - visit. It is a short detour from the Kaza-Manali route.