Over the years, I have gone most months.
I've been in December when it's nice and warm during the day, and also when it's just downright cold! Like, not fun cold.
January, I've been when it's okay and nice in the sun and warm, and years ago, when the high was 50 degrees F. Like winter coat cold. To me.
July is one month I refuse to visit. Check it off your list. Like it was ever on it.
Our spring break trips are normally March - this year was particularly hot and humid - not the norm! Hot like you want to swim hot! We enjoyed it (like all trips!).
If you can do late fall, you'd be at the Food & Wine Festival. Fun.
I don't know what weeks work for you, but honestly, if you can avoid July, you're good! We spend a lot of time at Epcot in the heat - nice pavilions and countries to explore!