First off, where is the 20k difference each year going to come from? If that is pocket change for your family, well then, fine. If it means you need to take on the standard federal loans ($5,500 freshman year, $6,500 sphomore year, $7,500 junior year, and $7,500 senior year) while you would have had no debt for GT, and your family can scrape together the rest, well then fine. But if it means you have to come up with a cosigner to take on more debt than that and/or your parents are going to have to go into debt, then no, it’s not fine.
I understand the temptation for a NYC area resident to stay close to home at Columbia, but run the numbers carefully. You don’t want one cent more of debt than you absolutely need. Pick up the phone and call Columbia. Talk with the financial aid office. If you commute to save on housing costs, how will that change your aid package?