Congrats on your admit and prospects!
I see you have registered a few years ago!
Booth and Kellogg names are stronger as brands and have some benefits when it comes to recruiting... however, during the normal years that requires staying close to the campus and shooting for interviews, meetups, coffee chats, etc in person. If you are in CT, how likely are you able to come down to Chicago for a Thur afternoon reception? or something along those lines? (This is the recruiting side of things).
Also, would you be recruiting in New York? East Coast? Again, Booth and Kellogg are very portable names and you can take them with you anywhere but it is nice to be in your own back yard and network with a bunch of Stern folks who are already on the east coast and could refer you for a job in their company right now. Again, not sure how useful that is to you.
There are a few FT students from Booth, Kellogg, and Stern but I am not sure I can tag anyone from the PT programs.... I would consider Brand vs. Recruiting vs. Logistics. People travel for PT programs all the time (a segment of folks but is it worth that effort? - is that going to make you happier and perform better or only make you miss out on opportunities, tire you out, and make you sleepy in the class?)