When and where should I go backpacking in Yosemite?

I’m planning a trip there this year and can go either early August or late September, which is better for the high country? Also I want to plan some remote backpacking (i.e. not on the valley floor) and am trying to conjure up a 4-5 night backpacking trip plan. My party is pretty fit and up for a challenge… anyone have any experience or ideas for us?