Columbia and the surrounding area

<p>I'm planning on applying to Columbia for graduate school in IE/Operations Research. I just had two questions, although not related.</p>

<ol>
<li><p>How tough is it to get into the graduate engineering program at Columbia? I'm not talking in terms of scores and grades, but in more relative terms. I know Columbia is a terrific school, but I don't see it at the top of engineering graduate programs (correct me if I'm wrong). How is it compared to the 'very' top engineering grad programs in my field, such as GT and Northwestern, regarding admission?</p></li>
<li><p>On a seperate note, for those who go to graduate school at Columbia, where do most people end up living? I know there are many choices, but I really don't know the neighborhoods that well, and I'm curious what a popular choice of residency is.</p></li>
</ol>

<p>Any input is appreciated!</p>