There are a million things to do and see. Balboa Park, along with the zoo and the museums, the beaches of Coronado and the strand, the coves of La Jolla for kayaking, the sidewalks surrounding mission bay for skating, biking, running, you name it...
If you're moving to La Jolla, don't forget to check out the seals at the Children's Pool, and also Torrey Pines State Park - there's hiking trails there, as well as a nice beach. La Jolla Shores is a great beach also. The Scripp's Aquarium is also in that area.
Downtown, be sure to check out Seaport Village and Horton Plaza and the Gaslamp District. And you might want to visit Cabrillo National Monument at the end of Point Loma - that's not really the right time of year to visit the tidepools, though, but you can learn something about the history of San Diego, and if it's clear there's a great view from there!
And as others have said, by all means check out Balboa Park - there's an amazing number of things to do there!!! No way to see it all in a day or two.
In the Old Town area there's also Presidio Park, and you can take a tour of the Whaley House (supposedly haunted).
I've been told I'll love it. Few good friends out there so I know I'll fit right in with them. I'm going to be working right across from Torrey Pines so it will be easy to visit during lunch and such for short walks.
Heading out there around the 18th of June. Maybe sooner, possibly that Monday before it. Once that weekend is over there really will be no reason for me to stay here anymore. Driving out...
San Diego is beautiful. Our girls who are about your age now, were born and raised in NJ and moved there after graduating college. One worked in LaJolla for a long time. Both work in San Diego now.
Whenever they host anyone their age visiting from home, they usually include the zoo, a Padres game, La Jolla, downtown and a trip to the Del Coronado. Since you've got two weeks, you can drive up the coast and tour the beaches even stopping in Anaheim/LA for the weekend, which they tend to do to see friends.