Having trained in NYC I know that many of my classmates have found jobs in the area without much difficulty. Working in the city proper tends to pay less, so many take work on Long Island, the northern suburbs, or *gasp* New Jersey. That said, I think there are also decent prospects in the city itself if you are willing to work for a little less.
I got a job in Seattle, so it is possible. However, I found there were far fewer openings then I would have liked, although I didnt have any inside information about the region so that may have been why. People there tell me though that the prospects are going to become slimmer in the future as last year many docs took left traditional jobs to work in many newly opening urgent cares but now things are returning to a balance. Plus I am sure a lot of the grads from the new Seattle program will try to stay local when they come out in a year or two which will saturate the market further. Always has been a tough market up there, it seems.
Dont really know much about the Boston area but on the whole it is always easier to find a job in the area where you did your training. .