Grand Kids to Disney in June

Probably your best bet to start off is go to mousesavers.com. They usually have info on all the current discounts, which generally is not many or not that big. Our experience with Disney is about the only way you get discounts is by buying multiple days at once, with 4 parks you really need a multi day pass to see all of them. For other places you can sometimes get discounts when you buy online in advance.