In my opinion the best time would be end of June as you will still find a lot of glaciers intact and a lot of snow on the mountains and on the path to Dodipat Lake, the contrast of green and white is just awesome. I visited Dodipat in the last week of June last year and, it was just great.
This year we are planning a trip to Neelam Valley and also in the last week of June i.e. from Lahore to Muzaffarabad to Sharda to Kel to Chita Khatta Lake and back to Sharda and then Naran via Noori top. If any one can help us in getting any jeeps on rental from Muzaffarabad or Rwalpindi please reply or mail me. If we could not get the jeeps on rental we will have to reverse the rout and start from Naran instead of Muzaffarabad.
Thanks and regards