Is there anything an aspiring physicist can do that they can put on an application that would stand out? I've heard of people building their own particle accelerators, but what would you suggest?
don't do anything just because it looks good on an application.
because they'll see right through the BS.
The only person I know of who's built a particle accelerator was Michio Kaku, but there are plenty of people who've gotten into MIT who never did that. If you're still in your junior year, take your AP Physics/Calculus courses, do well in them, study hard for the SATs and ACTs, get acquainted with whatever programs look good to you when you research schools online, and work on extra curricular activities related to science. Write a darn good personal statement that shows you love physics too. You may not get into MIT, but if you're reasonably successful so far and continue to build on that success, there are plenty of good schools who will be happy to have another physics major (since the average graduation rate for physics majors is 12 per year per school).