I answered a similar question on this recent topic:
As said there, June is not a bad time to visit, not as bad as often stated about the early monsoon in my opinion. That said, there are better months, ones without as much chance of rain and clearer skies. Given the choice, I would visit in the winter months because of a better chance of clear skies (including low humidity for sharper mountain views), drier weather and fewer visitors than the peak months in spring and autumn (March/April and October/November).
Welcome to Nepal in advance. Like sir Scoodly said earlier, Spring and Autumn months are the best times to visit Kathmandu and Pokhara. But still, one can never be sure that some months might have different weather than expected. If you are coming this mid June, you might be able to see the good view of the Himalayas since it's raining 3/4 days a week. As we all know, the next morning after the rainy night usually offers a good sunrise view and the clear view of the snow capped peaks. Still, all the best.
Gokarna, Nature Lovers Treks