So here are the things to know about PhDs:
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The rankings are different than the UG rankings, and they even vary by specialty within subject. One CC parent whose daughter went to Cambridge (UK) was appalled when she turned down a PhD offer from Cambridge in favor of a strong, but definitely lower tier than Cambridge university- but that university was where the actual top expert in her field was based, and that expert was to be her supervisor. Doing her research under him meant that every door in her field was open to her. So, if you have ‘prestige’ goggles on, be aware that what you see as prestigious may change as you grow in your field.
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A PhD is a research degree, and your demonstrated ability to do research will matter a lot. PhD admissions is completely different than UG admissions. Your actual expertise and your LoRs will matter hugely- so focus on getting research positions! You should already have applications for this summer out- but if you don’t, get on it now. As a first year, your best bets are in-house, but you might as well start applying for REU’s and similar. I’m not exaggerating- I have sat on PhD application review panels where a student’s summer experience using a methodology we were interested in was what tipped the balance between a couple of closely matched candidates.
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Don’t diss your uni! It’s top-10 in your field, and in academic circles (as opposed to friends, family & neighbors), people know- down to specific profs- who’s strong and who isn’t. And, as the example above indicates, PhD offers are closely linked to the fit between the student and the research that the department is doing. So, you could get to application stage and look at what the (say) Columbia people are working on and realize that what the NYU folks across town are doing is much more interesting to you.
tl; dr- stop worrying about whether east coast ‘elitism’ is going to scupper your grad school options, and focus on learning more about your field & whose work you find interesting!