Autumn (October-November) is the best time to visit Nepal. As the monsoons would just be over, the country is lush and green. During this time the skies are clear giving you a crystal-clear view of the majestic Himalayas, and the air is crisp and pleasant. Besides autumn is also harvest time and the season of festivals.
The second best time is February-April. However both these times are also peak tourist season. If you don't mind the weather too much you could always opt for the off-season, which is December- January. The monsoon period is ideal for visiting the rain-shadow areas like Mustang and Dolpo.