I had a previous post a few months back about India on a RTW, though since that plan was scrapped

myself and my girlfriend are going volunteering in May and June of next year with some travel time on each side of it.
My volunteer destination would be a couple hundred km's NE of Delhi- getting into the Himalayas. Now realizing the monsoon starts about june-ish, how bad will the weather be (rainwise??) I was reading a travel book on the area, but it mentioned that the trekking was to be done in this season.. in the rain??
What areas in somewhat close proximity Delhi would be good for a weeks travel in late april (i know its a steamer!) and early july.. thanks for everyone's imput!