The next best time  is from December till February, when it is winter months; with cool dry days, colder nights but clearer skies, affording good visibility.  It is also the best time if your trip covers lower valleys.

And thereafter June and August is okay, when the monsoon is mild with few occasional drizzle.

July and first few weeks in September are generally the wettest. But even these periods  has its own charms and perks. For instance, when monsoon is in song, it bring joyous rain that carpet the valleys and slopes with greenness, it injects a new lease of life to vegetation to flourish untamed and blessing for intensive terraced rice cultivation. It’s a visual treat to see farmers in motion, be it art of sowing, ploughing, or the children playing in the rice field.