Go during may or June (basically the summer months). Of you want to see the winter Spiti, then its best to reach Spiti by October end or November because by December all the roads to Spiti are mostly blocked due to snowfall.
If snow is what you crave for, then December - January from Shimla side to and fro because rohtang pass closes in winters.
But if you wamt best from Spiti valley and experience it to its full, then summer months is what you must take into consideration and complete full circuit from Shimla to Tabo to Kaza to Lahaul to Manali . Estimated time for full detailed trip will be 12-14 days.
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