You don't HAVE to do 4th year at affiliated sites. But if you want anything other than what they hand you, you need to arrange it yourself, either by VSAS, a residency's own visiting student program, or personl connections.
Graduation requirement for 4th year is 4wk EM, 10 wk IM, 10wk Surgery, 16wk elective.
The quality of your 3rd year core rotation could in theory affect how well you perform on the Sub-internship. Other than that, I dunno if programs look into where your 3rd year rotations are.
I don't know how geographically competitive NY is. If you have stellar board score, and have connections to the region(grew up in NY, family in NY), it may not matter a whole lot. But it really depends on programs and specialty you want. Some programs favor students who's done a SubI there, while some could only see you as disappointment if you are better on paper than in person. Its a double edged sword.
I want IM residency in one of the most competitive regions in US. My board is decent but not stellar. So I have 4 SubI scheduled outside the school's territory