San Diego is one of the most interesting California cities. Although your enjoyment of its many attractions depends on your tastes, I would highly recommend the following:
Balboa Park is one of world's finest zoos. Although you can make it through the park in about 2 to 3 hours by riding the free open air busses, it's much more interesting to walk it. This will take at least 5 hours. The snake house is at least an hour.
The Star of India, is an iron clad steamer/sailing ship moored near downtown San Diego. It's inexpensinve and a nice tour.
If you haven't selected a place to stay, be sure to check out on-line Harbor Island... it's a manmade island directly across the freeway from the main entrance of Lindberg Field, San Diego's airport. There are several hotels on the isnald and it faces the inlet ot the U.S. Naval base. War ships going to and from the Pacific Ocean sail slowly just a few hundered feet away. At the end of the island is Ham's Lighthouse with the best Margarita's in San Diego, in my opinion. Also on the island is a marina with an excellent restaurant... The Boat House is tucked out of the way in the marina... but worth the search.
The original Sea World is in San Diego, and also worth the effort...
Of course, you're only about an hour's drive from Tia Juana, Mexico, but it's not for the faint of heart.
At any rate, welcome to the U.S.!