I love
Disneyland during the first week or 2 of June. Its my favorite time to go. The schools are definately still in during the first week. During the first week usually on thursdays they have a grad night where they close the park early.
So since they extend the hours from closing at 8 to 11 during week days they will close the park at 9 for the grads to come in. I usually make alternate plans for that day so I can take full advantage of all the hours of the park.
The weather like others have said "June Gloom" breaks off by noon and get toasty but bareable warm. It cools down in the evening so you will want to wear longer pants and possibly a light jacket. But during the day you can wear short and tank tops and splash and get wet on all the water rides and dry out in 20 minutes.