OP, take a look at University of California: StatFinder
to see a more detailed view of how your stats compare. The most current admissions cycle listed is for 2009, and you can only look at either California residents or all applicants, not OOS applicants alone. Still, some useful information.
UC admissions doesn't consider demonstrated interest, so you don't need to worry about not being able to visit. Your stats are in range (though you'll want to recompute your UC GPA--you are OOS, so remember you can only weight AP courses). As an OOS student, the thing that is most compelling is if your family can truly afford to pay full freight for UC. Unlike highly selective private colleges, the UCs (like most public schools) don't give a fig about how many students came from your high school, or if other students from your school have a 2380 while you "only" have a 2340 or whatever.
Demonstrated interest is one of the most important things colleges look at
Many schools, especially the most selective, don't care about demonstrated interest. You can find out if a school does consider it by looking at the school's Common Data Set. Some will say that it's "considered", at most. Your GPA, test scores, and the rigor of your schedule are far more important.