Congratulations on getting into Booth and Columbia!
There is obviously a big component you are not accounting here, called life. That will probably account for 50%+ of the success of your experience at Columbia and Booth. I feel most of the points outlined points barely move the needle one way or another.
If you leave Chicago for 2 years and then come back, you will lose your network, friends, and connections you have today and you will have to work hard to re-establish them. So while I applaud you for wanting to challenge yourself and looking for a new exciting experience, it won't come without a price. If New York excites and you have an itch, then perhaps that's where you should go. At the same time, you are not the biggest fish in New York, unlike how you would be feeling in Chicago with Booth. You would be competing with HBS, Tuck, GSB, Booth, and everyone else who comes to New York to recruit.
P.S. at your stage in life, it makes perfect sense to explore, to try new things, and to do it. You won't have many other opportunities to move again - you will have a job, bills, loans, and then comes family, kids, school districts, and all the fun things that will tie you down for good. If the idea of spending your entire life in Chicago makes you feel uncomfortable, you should go to Columbia. However, as a person who has no skin in the game, my indicators point to Booth.