So, my absolute dream school is Stanford (of course). I recently watched a video on how they rank their applicants and how heavily they weigh an applicant’s intellectual vitality. I’d say my vitality is not up to par with the Stanford admits. I’m a junior, so I have a very small amount of time to improve this. Some of the things that I’ve done that could be examined as intellectual vitality are competing in the academic super bowl on the math and fine arts team (we didn’t make it to state and the video said that Stanford likes students who learn for the sake of learning not to beat the competition, so this topic for an essay could be counterintuitive) and taking flying lessons to ultimately get my pilot’s license (I’m not sure how i could adapt this into intellectual vitality). The video that I watched said that doing and then proceeding to publish research done at a university is what a student needs to receive a high vitality rating. What can I do that is an equivalent to this? How would I go about doing research at a university when I’m in high school? I actually do genuinely enjoy learning, but finding opportunities where I live is difficult.
Was this video published by Stanford, or by one of the crazy-intense admissions hawks? It makes a difference. Usually colleges will take context of opportunities into account–the important thing is to challenge yourself as much as you realistically can. If a school doesn’t offer APs, a college wouldn’t fault the student for not taking any. If a student has to work to help support their family, a college won’t fault them for not spending enough time on ECs. A lot of college-admissions-tips videos verge on hyperbole, because if they can make you stress out and scramble to “improve”, it means more business for them.
If you’re really concerned that Stanford will think you’re not doing enough, you could use one of your essays to discuss your lack of opportunities. Writing about your longing for more intellectual stimulation and research opportunities is a great way to demonstrate vitality–and could tie in nicely with a “Why Stanford”-type essay.
Lack of opportunities doesn’t equal intellectual vitality. An essay that admits you didn’t find opps on your own is the opposite of what they want to see.
It’s not just research. It’s about how you approached your education.
read books
I think there is a general misunderstanding for what “take context of opportunities into account” may mean. In this period of free MOOCs and free online courses from top universities – how to say that a student was restrict in opportunities? If you need to ask how you should improve your “intellectual vitality”, then you may need to realize that that if you worry about being presentable to Stanford – eventually you will lose your own voice (and consequently lost in a sea of applicants).
Read.
Give yourself a goal of one book per week. Start small , IE., short (Persepolis, Letter from a Birmingham jail, calvin&Hobbes, I am Malala, Agatha Christie, Ender’s game, or even a couple Famous Five or 'unladylike murders ’ 
.) Most important criteria 1)you think you can read it in a week and 2) you WANT to read it.
Then go from there, getting more ambitious when school ends.
Read every time you can carve out a few minutes for yourself.
Create a reading list for yourself from now until Fall start again - roughly 12 -15 books. Choose books you GENUINELY want to read. Browse all aisles in your library. Look at corners and shelves you haven’t explored yet. If you don’t love a book, you could try to finish it but alternatively just pick another one. It doesn’t matter. (One of Daniel Penac 's Rights of the Reader struck me because until then it would have seemed blasphemous : 'you don’t have to fibish the book. ’ You read for pleasure. If you find no pleasure in reading that book, find another one.)
Before you start on this project : Try to write an essay to yourself as to how/why you chose these books. Then, read. 
Don’t create a list ‘to impress’. If you follow someone else’s list, it won’t show intellectual vitality, just your ability to copy CommonCore or Summer Reading at your school. If you pattern your list after your interests, it’ll be absolutely unique. Thus, you’ll have an awesome and unique story to tell about something you love.
And it requires zero special resources, just a public library.
Also, borrow _How to be a high school superstar _ by Cal Newport.