> it still blows my mind that Muslims in New York City face roughly northeast to point toward Mecca

It never occurred to me they would face the shortest distance to Mecca. I've looked it up and apparently it's a point of contention in North America, although the great circle seems to be standard. Interestingly there are landmasses around the antipode of Mecca, which means your direction would vary wildly as you travel around.

I like the idea of there being a place on land where a Muslim can look anywhere, and be looking toward Mecca.

But apparently, it's the middle of the ocean, although there does appear to be an atoll very close by: https://en.wikipedia.org/wiki/Tematagi