I guess any advice would have to hinge on exactly what it is you'd like to do. I, too, considered medieval studies programs, but wound up applying only to English programs because much of my interest in medievalism has to do with how it's represented in different time periods or genres- in other words, I'm not interested in"pure" medieval studies. Would your research benefit from the ability to draw on resources across a number of medieval disciplines (i.e. history, music, in addition to literature)? If so, think about it. I'm sure, also, that Cornell would encourage you to take a bunch of English classes, and, though I don't know much about the school, I'm willing to bet there's some substantial crossover between the Medieval Studies and English faculty; you'd still have access to English department resources.
One of the reasons I applied as a medievalist is because I was told I would be much more marketable both as a PhD applicant and as a job applicant a few years down the road. Apparently, every department feels obligated to staff at least one medievalist. A Medieval Studies PhD (as opposed to one in English) would probably qualify you to teach in a number of different departments and in the end might make you even more marketable than someone with a straight English PhD. Then again, the teaching/hiring landscape is obviously undergoing some economically-influenced changes, so who's to say what will be marketable six or seven years from now?
Regardless: Cornell! That's awesome. Give them a visit.