I reached out to Mixpanel (mixpanel.com) last spring as a high school senior (with no professional programming experience, but a couple of decent sized projects and a decent amount of experience). I ended up going through their interview process, getting an offer, and then going out to San Francisco and working at Mixpanel for 3 months. The experience was indescribably valuable, and if you think you are experienced, I'd definitely recommend going for it. Even if you don't think you are experienced enough, I would recommend going for it, because worst case is you don't have an internship, which is the exact same as if you don't do anything at all.

The "Who's Hiring" monthly threads are a good place to start looking.

First - it's impressive that you're already thinking about this. I definitely wasn't looking at internships back in high school

When I was at FB, several of the interns had just finished high school, so it's certainly doable to get a top company offer - same goes for start-ups. It's just a question of emailing them and having the experience - past projects, etc - to be interesting. Same advice as I'd give to a college student.

Try to find a local company. Advertising companies usually do some sort of web presence thing for their clients. That's a place where you could provide value.