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.

it's totally worth it when you get the discount. I was on hold last week for 3 flipping hours. And when I FINALLY got a live human, it was like the best thing ever. And on top of that, I saved $ 909...so it's worth it. If you have speaker phone, just put it on speaker and go about your business.....Good luck !!!! 
