HTML and CSS are part of web development but they are not programming. They are excellent skills to learn, though. I would recommend just about any student have at least a little learning in that area.
It would be javascript rather than Java programming that would be used in web development. Javascript programmers are in high demand so that is a great skill to learn.
HTML + CSS + javascript can be satisfying for students to learn because those three together are the core of how websites are built.
Code Academy is a good resource. You are correct that it is aimed at adult learners, but I’m not aware of anything that would leave out a high school student.
Let me ask a someone I know who has a business in that industry and see if he has any recommendations. I’ll let you know what I find out.