I would say with the ever increasing length of the school year and "summer" sports, if we try to accomodate a more family friendly time, we are pretty much down to 2nd week of June through last week of July. June is usually not as hot as late July and August in the south, but still pretty warm, especially to you "Northern Aggressors." Spring Break would be cooler, but no way could we line up everybody's spring break week. Hell, spring break in Alabama is different weeks depending on the county you live.
I'm fine with it whatever week as long as school is out (unless my wife and kids decide to not go again, then I don't care when it is.)
**Edit. Charlotte again would be fantastic.