any time i've gone solo, it's been in late october during F&W
found that i really enjoy myself and my "alone" time more when i can leisurely graze the food booths, enjoy the shops in each WS country, bypass all the rides (that my DH and DS insist i join them on....) and shop shop shop!
the weather at that time is also pleasant, not as hot/humid as during summer or even september - less rain - crowds manageable (but when you're alone, you're in control of what you do, with no one else to cater to, so you can dawdle at your own pace)
honestly, my favorite times were when i'm there all alone, walking from epcot to mgm along that path, or riding the peoplemover over and over, or just enjoying the lushness of AK (with no one to rush me or roll their eyes when i just want to sit and take it all in)