Which High School for the Arts?

"Strongest visual arts program" is very subjective, and in fact "animation" may not be considered a visual art in a high school curriculum. My first suggestion is to drill down into what your child is really looking for within her high school curriculum, and compare that to what these schools offer. I have a current high schooler, not that artsy, and a rising 9th grader, who is. My elder child is at a relatively well resourced public high school that requires a year of both a fine or performing art (2D & 3D art, photography, music, dance) and an applied art (graphic design, engineering design, etc.) to graduate. This complies with but goes beyond the UC A-G requirement for one year of VAPA. Thus they offer multiple options and sections of art classes every year; they have to, so kids can meet the graduation requirement. There are also multiple student-run art clubs at the school focused on different types of art (anime, etc.). 

Another factor is how many AP art subject classes the school offers each year, and what grade levels they are open to. (I know there are some at my elder child's high school, at least AP Art History and AP Visual Arts, but they aren't interested in that pathway so I don't know details) This may or may not need to be a deciding factor but could be a proxy for support for the arts. I have the impression it is not unusual to alternate offerings each year (ie., there's only one advanced art teacher on the faculty who teaches AP Art X one year and AP Art Y the next year).

My artsy rising 9th grader is considering that same school and is comfortable with the amount of art classes available each year, but also considering a local private high school (not on your list above) that offers Visual Arts as one of only 4 electives 9th graders can choose from, followed by a sequence of Honors, Studio, & AP visual arts in subsequent years. There is one student run art club. My student feels fine about this as they currently consider themselves to be an exclusively visual artist; I personally think the offerings are a little slim but I think it's a well established & funded pathway that's solid.

Unfortunately you've just missed exhibit season where both the schools I mentioned above, and probably all the schools on your list, host public receptions for the end of the year with student work on display. We have been to the one at the public school two years in a row and thought it was super - clearly a range of artistic abilities but many fun projects. Sadly we missed the one at the private school. But attending one of those if you can, is a great way to get a feel for the art program sequence through the years (the 9th grade projects are different from the 12th grade projects!).

You don't mention OSA but that would certainly be a school to look into if art is driving the train. I was not comfortable with its location so we didn't pursue it as an option for my artsy child.

Finally, animation often falls into a different bucket than art - vocational training or workforce internships. Some public high schools have "academies" that do a lot more hands-on skills based work and if animation is a top priority for learning within high school (as opposed to the many classes outside of school that are options), you may want to look into those.

If your kid is interested in animation and character design, I would at least glance at OSA. Both my children are in their Digital Media program and I can attest that their animation and character design opportunities are strong -- one of my kids just got a special recognition for character design. I know you say you are interested in "independent" (i.e. private) schools, but OSA is a charter and thus has more flexibility than mainstream public schools as well. I know some people are concerned about the location but we've been attending since middle school with no problems. I know others worry about their academics but they're solid if not sparkly in my experience. 

I don't know a lot about Lick-Wilmerding but I work nearby and my partner's company contracts with them for audiovisual tech, and I have generally good impressions of the staff and students.