<p>NYC is not actually as safe as it is purported to be. Larger cities have much more random crime, as I have shown elsewhere (e.g., less than 50% of the 500-600 murders were ever solved in NYC). Smaller cities a greater % of the crime is between acquaintances/boyfriends/girlfriends etc (in New Haven's case, 100% of the 14 murders). In NYC, the "per capita" crime rates are lower than most cities but that's because there are huge concentrations of people living within the city borders, in fact, mostly in suburban areas on the fringe or areas where immigrants are packed in very tightly such as Chinatown. That lowers the average rate, but it does not make the median # of crimes per given area/per given person any lower when you are talking about a typical neighborhood. I mean, after all, that city has 500-600 murders per year and tens of thousands of other serious crimes. In Boston, it's even worse, because Boston has a higher per capita murder rate than both big and small cities in many cases - higher than either NYC or New Haven, for example - yet still has all the random crime problems, with only 30% of the 80-odd murders solved.</p>
<p>When you're talking about Columbia and Yale, they are both in cities. If you go certain directions, you run into very wealthy areas, while if you walk a ways in other directions you may run into a poorer area. You need to have street smarts and a sense of your place in the city. The particular differences between the two are that Yale is in a much more central, vibrant part of its city (the downtown, right by the city center and city hall, surrounded by hundreds of places to go) whereas Columbia is in a more remote district (with a few good restaurants and stores, but not nearly as much), basically in Harlem (although real estate brokers call it something else to sell houses), and you need to take a loooong subway ride to get anywhere cool.</p>