I live in the L.A. area, and June can be sunny and warm or cloudy and rainy. As previously mentioned, we call it "June Gloom". It's really hit and miss. It won't be too hot yet. The GC is the resort which is most the the WDW resorts and is a great hotel. We have an attachment to the Disneyland Hotel as it was the only official Disney hotel for many years. The PP hotel is okay. Be aware that the GC is the only hotel built by Disney. The other two were built by other companies and refitted by Disney. They are nothing like the WDW resorts, but still very nice.
Universal Studios is a good trip if you are interested in movies and TV. It is an actual working studio, unlike the amusement parks in Orlando that want you to believe they are real studios. If you like Desperate Housewives, CSI, Jurassic Park, Psycho, The Grinch, War of the Worlds, and many other shows, they were/are filmed, or have had scenes filmed right at the studios. You can take the tram tour and visit many of the sets- the backlot is huge.
You can also see the real Hollywood (take in a Disney movie at the El Capitan Theater and have a meal at the Disney Soda Fountain).
Depending on when you visit, you can also see a show at the Hollywood Bowl, the famous outdoor ampitheater.
The Getty museum, the Griffith Park Observatory (cafe is catered by Wolfgang Puck), the beaches, Sea World, Magic Mountain, and Catalina Island are all easy day trips as well.