There are several guesthouses.

Norling Guesthouse
150 Rs for a basic room, 350 Rs for a better one with bathroom (hot water from geyser)
near the entrance to the village

The best place in Kibber with a friendly owner, good restaurant and a great balcony. Rooms on the 2nd floor have bathrooms. Beer available on request.

Tashi Zom
500 Rs for great double rooms (fully wooden, large windows/good sunlight, nice views of Khardung peak etc); good bathrooms attached to all rooms, with geysers with hot water
just before the entrance to the village

The warmest place in Kibber, a bit out of the clutter of the village. Interesting owner though he might not always be around, nice construction, VSAT Internet + wifi at a price. Reasonably good restaurant. Might be a good idea to sleep here and go to Norling for food. Have a family room big studio with tandoor for heating/cooking for Rs 1000, prices discounted for all rooms if you stay more than a few days.

Serkong Kibber Home stay
inside the village, not far from the bridge

A great source of village culture and natural living. Located in the heart of the village. Many comfortable rooms available and some of the most delicious home cooked food in Spiti and beyond.

Pitch a tent in the grassy meadow opposite the Kibber Youth Council cafe, they charge a nominal rate for it