Best weather? Lowest crowds? Most entertainment? It all depends.
o End of June - both in 2010 and 2011 this is likely to be the busiest time of your time period. It will have the coolest temperatures. It will have max park hours and max entertainment offerings. Refurbs will be zero or minimal. Unblocked AP holders will pour into DLR to ride new Little Mermaid at DCA and Star Tours 2 at DL.
o July and early August - summer crowds but no AP holders - they are blocked. So crowds should be busy but manageable. No refurbs. Max hours and entertainment. Hottest temperatures in August.
o Late August - return of AP holders after blockout means large crowds. Still hot.
o September - up through Labor Day larger crowds. After Labor Day big dropoff in crowds. Also refurbs start including Haunted Mansion down for most of the month. Space Mtn goes down for a few days to add Ghost Galaxy. Often Matterhorn goes down. Crowds are less and parks hours are shorter. Entertainment reduced on weekdays. If low crowds are your highest priority then Sept is your month. Still hot but not as bad as August.
For background info see
"Understanding AP Blockouts and Impact on Crowds"
http://www.disboards.com/showthread.php?t=2365983
"Historical DLR Park Hours, Entertainment and Refurbs" -
www.disboards.com/showthread.php?t=2291124
"Detailed Weather Data for DLR"
www.disboards.com/showthread.php?p=23004158