Really depends on what your priorities are, in terms of drinking and going out and whatnot. I don’t have a fake, but I usually only go out with friends who are much older and I do not go out often enough for it to be worth it. I also don’t drink and, if I did drink, I would ask my older friends to grant me access to booze.
I would recommend getting a fake if you intend to go out every weekend with a younger crowd (like freshmen or sophomores and probably juniors as well)—people who are younger (especially those who go to colleges that are as insular as Columbia) tend to carry themselves differently than people who are older and bouncers usually pick up on those subtle differences because that is their job. If you’re going out with people who are older (like, seniors or college grads), that’s tricky—on one hand, if you are with a group who carries themselves in a more mature way, you probably won’t get carded because you will blend in, but on another hand it would really suck to get dressed up and to travel only to get turned away at the door while all of your of age friends are admitted, so that’s up to you. I would not recommend getting a fake if you just want to buy alcohol to drink in your dorm because you really could just get an of age friend to do that for you.
I personally recommend making older friends as a semi-alternative to a fake because (a) they might give/buy/sell you booze and (b) if you walk into the right bar with people who are older (especially if they’ve graduated from college and/or especially if the bouncer knows them well), you are far less likely to be carded. There are lots of bars in NYC that are pretty lax on carding, so ask around to find out which ones do and don’t card.