I'm chiming in to caution you against choosing one medical school over another based on the date the school starts. It may not be ideal for your short term relaxation, but it's inconsequential when considering the long-term: where you want to spend the next four years.
In full transparency, I'm planning to start at Jeff this summer. So, now I'll try to sell you 🙂 . I share some of your thoughts. I also have most of my network in/near NYC, but it's close enough to Philly that it's not an obstacle. I'm eager to do research, too. On one hand, you might point to Einstein as having more NIH $$, but on the other hand, there will probably be less competition for research opportunities at Jeff since not every student does it. And, being in Philly, there are plenty of research opportunities outside the institution. Some students do research at Penn. Finally, I think you'll find Center City to be a cooler place to live than the north Bronx, and when you factor that in with the cost difference, I'd say join me at Jeff 😉 .