I went early April last year, it was busy but not anything I'd consider extreme, but definitely busier than my preferred time of year for visiting which is late August/early September. I think next year with Easter being quite early the very end of March could be a little busier. You've also got Spring Break to contend with, but again it seems better to go early March as less schools tend to have their breaks the first week in March from what I recall.
We are choosing to go late April in 2015 as most schools here have started back before we fly out! Or at least that's what my research is telling me!