Monsoon season in Nepal is month of June, July and August. There are several trekking region in Nepal which are rain shadow area. Upper Mustang, Annapurna Circuit, Upper Dolpo are the major trekking destination during monsoon. Those areas are less vegetation similarly as Tibetan plateau. It receives very little rain in those areas; at the same time other areas of Nepal get extremely heavy rain can be whole day. Less vegetation areas get greenery after little rain, which makes area more charming that is even benefit for trekkers because greenery provides more oxygen which caused easy to breath at high altitude.
Annapurna Circuit Trekking in Monsoon season: the upper part of Annapurna circuit like Manang part is less vegetation areas get less rain. Starting part of the trekking get heavy rain but still trekking at the area does not get block or disturbance. The regular trekking starting from Besisahar, reach at rain shadow area of upper Manang, climb to Thorong La and trekking ends at Lower Mustang at Muktianth Temple. Upper Mustang Trekking in Monsoon consider as main season. Plateau landscape get very little rain caused valley became greenery. It becomes more charming with panoramic mountains. Similar the Upper Dolpo Trekking is high Himalaya trekking also called rain shadow area. Similarly trekking to Limi valley at Humla, trekking to Rara lake are the best destination.
Many of other best trekking still possible to do during monsoon. Mountain views are often obscured cloud; temperature gets high, rains daily. You will get fewer crowds during that period. Annapurna region, Everest region and Langtang region still will be possible to trek. This is the main season Nepalese working at field. You will view real life of Nepalese peoples at this season. Sightseeing tour in Kathmandu, Pokhara and other major tourist cities do not disturb. Jungle safari in Chitawan, white water rafting tour is also suitable at the period of monsoon in Nepal.