My first two years I've gone to WDW we went in April. We usually go during Spring break (Chicago School Schedule), but since their Spring Break is the week of his birthday his Dad won't allow us to go (spoiled brat). I've always felt that I don't get to do a lot of the attractions/rides as I think I would. I'm also a late sleeper so early mornings and I don't get along. This year we're going in June (it's not going to be April with out Disney).
Hints for late nights in April:
Bring a sweater !!! If you're going to Illuminations or Fantasmic, it will be chilly. Chilly, Chilly, Chilly. You're teeth will chatter (at least mine did).
Also, pack a couple pair of pants. Jeans or sweats...last year was a very wet year and chilly time to go. Not fun when the DS has a broken arm.
Just remember to use the fast pass. If you can get the parks twice, (e.g. Epcot for Illuminations or MGM for fantasmic) alternate the Shows and the rides. If you see Illuminations on 1 day, do the attractions the 2nd day. I've been there twice and I still haven't gone the majority of the rides.
Hope this helps.