I'd cap it. I went to Rex Putnam High School but it is more often referred to as Putnam and Putnam High. Still a proper name. I think we get so caught up in things like this that we're not looking at the big picture, as in intent. This is clearly the name of a high school, and it will look like an error on the reporter's part to not cap it.
That's a harder one to decide on, but out of curiousity, I googled it and nothing came up as "Menlo High School" so I would not cap it either. I think if it were commonly referred to as such, I would cap it, but otherwise, no. So that's my two cents and it's probably worth about half that.
LeAnne, I cap it because of the same reason -- intent.
Up here, we have streets and avenues; numbered thoroughfares are always avenues, but they are 99% of the time called street -- 32nd Street. I always cap that. It would look wrong to not have it capped, and the intent is the road called 32nd, not the 32nd street in succession or from the accident or whatever.