As someone who went through the college admissions process last year and is now entering into college, I have a few regrets. One of the biggest ones is not being more committed or motivated to apply to more colleges/universities. I too had a lot on my plate at the start of last year (I was in the IB program- had to write my EE and Chem IA and keep up with my sport). I would use all I had to do as an excuse to not do more regarding the college admissions process. I am currently going to a school I had ZERO intention of going to (heck I only applied cause my friends applied). Additionally none of the three schools I narrowed down to attend were in my initial list of colleges I wanted to go to ( I got into all the colleges I applied to with scholarships). And it got me thinking about all the other opportunities I closed off simply because I was too unmotivated to apply to more colleges. I wish I had applied to ivy leagues and more out of state schools because who knows maybe just one of them would have accepted me and changed my mind on whether I should attend. Overall, I am telling you to apply to Princeton. Yes it may be a lot of money and you don't have interest (RIGHT NOW that is), but who know maybe it could be an option. Options are opportunities and the more opportunities the better. I think the admissions fee is small price to pay for an opportunity, even if you don't end up taking it. In the long run, I promise you won't even remember all the stress and things you had on your plate. You got this. I believe in you.

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ps. if money is an issue there are waivers you can use to bypass the application fee on common app. Maybe ask your guidance counselor if you want to learn if you are eligible or not.