Anytime is best time to visit Auli. Summers are very pleasant in Auli with average temperature around 15°C. June is ideal for all sight seeing, skiing and also for visiting nearby attractions.
You can visit Auli in Summers, and Winters but would advise to take caution while visiting Auli during monsoons as the path leading to Auli may experience landslides during monsoon in Uttarakhand.
Ya June is a good time to visit Auli but, the best season to visit Auli is all through winters. The main Tourist attraction in Auli is Snow Skiing and is best during November to March. May to November offers cool and pleasant climate and the right period to spend relaxing moments in the outdoors.