May is our favorite time to go. The weather is usually beautiful, the crowds are low to manageable.
2nd week of september was nice. It is still hot though, and it can storm (but it's like summer and it usually passes through quickly). Hours are shorter, and if you want to see Spectro/Wishes, you'll need to plan carefully. Park hopping is needed more than at other times of year. Also, there is a hard ticket event, Night of Joy, at the MK so it closes early one weekend. Not a big deal, but something to plan around or plan for.
We've gone a few times in March and April. The weather is usually wonderful, but crowds can be very bad. I've visited a couple of times in early march (1st-2nd week I think) and you do have to plan for lots of visitors, even if it's not around Easter.
This past year we went I think 2 weeks after Easter, the last week in April. It was pretty crowded, but not really a problem as we try to use fast pass and good planning. The weather was great! We did have a Grad weekend with an MK closing early on fri/saturday.