We go that time nearly every year, I would say as early in the week as you can. It starts to really build in crowd the closer you get to T-giving day. So the earliest day you can would be best option IMO. Plus do rope drop if possible to get a much time in before the crowds swell...
I'd LOVE to go at some of the less crowded times of year, (ppl say first week or 2 of Dec is awesome)... but I work at a school so summer, T-giving break, C-mas break or spring break are only times I can take vacations. But we have a blast regardless, and just go into it knowing there will be crowds. I know some ppl say that for them it feels just as crowded at T-giving as in the summer, but for us we find June/July WAY more hectic (with exception of T-giving Thur-Sun which is indeed slammed). Or maybe it's just that we avoid that summer heat that it just feels not as bad, LOL