The 50th celebration goes through May 2006. Soooo,
In Wisconsin the kids get a break at the end of October for teacher's conventions. This is a very popular time for many families to take their vacations. Do you have a similar time available?
Naturally, many people feel as you do about not wanting to take their kids out of school, so that makes the times when all kids aren't in school, very, very busy.
I think that around Christmas is a beautiful time to see the parks, all lit up, it's magical. Of course that's when 50000 people feel the same way so you aren't avoiding crowds. If you're lucky enough to have your spring break 2006 at a time when not many others have theirs you might do okay.
May 6th, 2005 is the official start of the celebration. I would avoid this week if at all possible. If you are thinking summer, it seems that it will just get busier as the year progresses so early June 2005 will be better than July 2005 (especially since the official anniversary is July 17th).
If your school year starts after Labor day, then the last week in August 2005 might not be quite as busy as the rest of summer.
I don't know how old your kids are and if you are dead set on not ever taking them out of school, but you might find that the more notice you provide to teachers the more willing they would be to help accomodate you. Then perhaps the second or third week in January would be good. Very low crowds.
Hope that's helpful!