It's kinda difficult to explain how crowded it is.... It's not as busy as mid summer, because many of the nearby schools haven't finished. It's not nearly as busy as July 4th.... but it's more busy than May, September, etc.
We go every year at this time...because it's not as crowded or hot as mid summer. Oh.. make sure you check out the salmon at Artist Point. Late May and early June they fly fresh salmon in from the northwest... The salmon is incredible that time of year!
If you carefully plan you park activities, and make effective use of FastPass... you will not even notice the corwds.
See you there!