Discounts?
Do you belong to AAA? Many places offer discounts if you show your card.
Or my husband's former company often had discount offers as one of their benefits - perhaps your workplace has something similar.
What to do on an extra day? Where, oh where to begin. . .
What is your family interested in?
"The beach"?
There are many. In June, of course, they will be crowded, and parking will be insane, unless you get there fairly early in the morning.
Kids interested in a surfing lesson?
Crystal Cove has tidepools. Also about a billion steps down to the part of the beach where they are, but they're really cool. Just remember that it's illegal to remove *anything* from the habitat. Look, take pictures, even touch. But leave the creatures there :-)
Last time we were there, we saw crabs duking it out over a piece of food, and a dead octopus. Memorable! Mention tide pools, and my daughter still talks about it :-)
Newport Beach/Balboa Island
Huntington Beach is Surf City, and there's a museum devoted to the history of surfing.
Laguna Beach - the summer art festivals don't begin until June 29, making parking perhaps a little less crazy :-)
http://www.lagunabeach.com/attractions/
Sports?
Yes, check out the schedule for the Angels.
Or the Newport Sports Museum. It's free :-)
http://newportsportsmuseum.org/about/
Art? History?
The Bowers
http://www.bowers.org/index.php/art/exhibitions_listing/c...
Richard M. Nixon Library and Museum
The Queen Mary
Science and nature?
The Cube! Discovery Science Center's summer exhibit will be "Wildlife Rescue" in addition to their regular features.
http://www.discoverycube.org/exhibits/event/wildlife-rescue/
Long Beach Aquarium of the Pacific
Santa Ana Zoo, Orange County Zoo, Tucker Wildlife Sanctuary, Upper Newport Bay Wildlife Preserve (mostly hiking, but there's a nice nature center, and you can rent kayaks)
This is just a drop in the bucket. If you're willing to drive to LA, there's additional great stuff.
Time to get thee to AAA for a TourBook, or start googling "Orange County Attractions" for yourselves :-) Perhaps making your own list of possibilities could be a project for your kids, and then the family can vote or draw from a jar for your final decision?