I think the core rotations have to be done at an affiliated hospital. It is possible to schedule your own cores but strongly not recommended, just pick one of the clinical centers and do them all there. Trying to arrange your own is risking a delay that can cost you later on in the Match. Save your away rotations for 4th year electives.
There are several in the NY metro area, and a couple in southern NJ as well which are probably even closer. Philly is like 2 hours on a $10 Megabus from Midtown. Easy peasy.
Also, don't pick your medical school based on the geographical location of their affiliated hospitals. You won't have time in 3rd year to do much else than study and work anyway.