I was living in the Union Square area--on East 12th Street and Fourth Avenue--in an NYU dorm, and after about a year and a half I recently moved to Broome Street in Chinatown.
I found my new Chinatown apartment online via Craigslist. It has three single bedrooms and a fully equipped kitchen. I share the apartment with two other people and each bedroom is close to the size of my old apartment.
Transportation in general was better before because the Union Square station was close by with several subway options, the place I go most often--work--is now accessible by not even having to take a subway--it's a 10-minute walk. In addition, there is a subway station about five minutes away at Spring Street.
Back in Union Square, I was constantly in the midst of tourists. Here, even though there are tourists along Canal Street, by Broome, it's mostly native New Yorkers. Surprisingly, they seem to cause more noise than the tourists in Union Square. The noise is mostly cars honking and people yelling because a lot of rushed people travel through Chinatown to get to work. But my neighbors in both buildings in both areas were great.
There is a mix of people who live near me--single, with families and of many ethnicities, particularly Asian.
One drawback is that the area is a bit rundown and my new building is very old as are most buildings in my immediate area. My building seems slightly dirtier than my previous one and sometimes the smell of food can be strong.
However, I save so much money that it is well worth it. The cost of most things in Chinatown is much cheaper, especially food--you can get a rice platter at some of the Chinatown restaurants for $6!--and it is fun to try out all the shops along Canal Street.