gavra, I never heard anyone refer to any part of Brooklyn (if not all of NYC) as anything other than in-town.
A Godol once told me that he thinks the reason New York is the biggest Makom Torah in c’l, is because the Yidden of York (England) were moser nefesh their lives al pi Kiddush Hashem, when the goyim wanted to force them to convert.
Some Yungerleit move elsewhere because of the cost of living in NY or for other personal reasons. But I would venture to say, more people from OOT move into NYC (Yeshiva, Shidduchim, Business, etc) than the otherway. I’ve met so many former out of towners now living in Flatbus (as well as other parts of Brooklyn and the City), that I couldn’t begin to count ’em.