You're fine either way, what an awesome choice you have...wouldn't underestimate how nice it'll be to have your own place with space tho. In St. Louis, you can legit live in a very nice apt for a fraction of what a mediocre apt will be in NYC. NYC is NYC, but STL shouldn't be slept on. Also, would ignore the idea of name outside of medicine, unless you plan on starting a company in the Northeast or something lol
Lastly, I think this is one of those situations where you can legit just follow your heart. If you're leaning Columbia, take that! They are equivalent institutions and unless the COL is a major con, then you may regret not going to Columbia if you're leaning towards it. Good luck!