Usually Monday and Tuesdays are good days becuase it seems more people are checking in or out on those days so the parks are less full. Last year we went the first week of July and checked in on Monday and I remember the park being quite slow the first 2 days we were there and then by Wednesday the parks were starting to get more crazy.
With WWOHP opening, things might change. This year we check in on Sunday and leave on Friday so hopefully this gives us plenty of time to relax and do what we want to do while there.