I am not sure where you want to stay, but there are some discounts through Magical Vacations for later June/early July. I don't think we can post links here, but just google them and they should come up first. Look under their July 4th offer.
HTH!
Amy
This is where I booked. June 18th - 25th. Discount goes thru the 4th and the room discount is around 22% by my calculation..So worked well for me b/c DD14 graduates middleschool and we have ALWAYS gone the 7th thru the 14th but this year this is a ceremony, a party etc and we weren't free until the 14th. So this discount period worked well and there is even a discount on the park passes too with this agency week.