For the past 10 years or so each summer my family would spend two weeks doing the Disney thing (we are DVC members) and we generally went in mid-late July.
Its very hot and humid during that time and personally I enjoy the fall or winter better, but summer does have its high points since there are lots of things going on (not to mention lots of other visiting families!)
I would highly recommend any of Disney’s on-site properties if you are looking to do Disney at all. They are IMHO, far better than most of the other generic hotels (Marriott, Hilton, etc) outside the park, though you do pay a premium for the magic.
Being the Disney fan (and freak) I am, I also enjoy Disneys beach resort at Vero Beach. IT is also a Disney Vacation Club property and is a very nice place to spend 4-6 days. Its about 1.5-2.0 hours to the South-Southeast of Orlando.