As my mother likes to tell me: do you, boo! If Columbia will make you happier for the reasons listed above (you like the faculty, students, and prestige), then go ahead.
Columbia is pretty hit-or-miss with graduate programs. I wanted to apply for their Urban Planning program, but the feedback wasn't all that great. And I wasn't impressed with their portfolio or professors. A lot of the people who I've encountered feel the same way, and those who accepted feel cheated out of thousands of dollars (not only on these forums, but some planning forums and discussion groups I follow).
At first glance, it seems like Columbia's grad programs are an afterthought. Money making scheme maybe, but definitely poorly presented.
If you're not pursing a PhD, then brand name doesn't really make a difference. Some will recognize Columbia and be really impressed, but most don't care. At the end of the day, your mileage will vary. It's what you make of it.