Shouldn't your research background be a lot more important than prestige when getting an academic job? It is a profession after all. Ohio may not be amazing, but it is decent. I attended a lot of presentations by faculty applicants back in my undergraduate and no one ever seemed to care what school they came from. We had a UPenn guy come in vs. someone from Lehigh (a regional school). All the students in attendance voted from the Lehigh candidate because he had amazing research, knowledgeable, personable and just fantastic presentation. The UPenn guy just did not seem to fit the profile of someone who can teach.
I don't think 100K+ debt is worth it for a Master while living in NYC (average 15-18K annual expense if you are lucky, I live there).