for all those moving to new york, especially with dogs - don't write off brooklyn! i know that everyone here has been talking mostly about manhattan, and manhattan is great, but brooklyn can be a fantastic choice for a lot of reasons. someone else on this forum mentioned that it would take 45 min to get from bk to school, but i can tell you it takes me about 30-35 min and i don't even live in one of the closest bk neighborhoods to manhattan (the closest would probably have you there in 15-20). i know people on the upper east and upper west sides who go to stern and have longer commutes.
brooklyn is generally a little bit cheaper (not always), but the big thing is you usually get a lot more space for your $$, which is great, especially if you have a dog. i actually have a real kitchen and a backyard, which i'd never get in manhattan at this price. ditto on my bedroom and living space. also, we have great restaurants and bars and all kinds of fun stuff. it's generally more residential in feeling -- less packed sidewalks and tall buildings. i like the craziness of the village but it is nice to come home to something a bit more calm and still very urban.
if you want to check it out, i'd look at: cobble hill, carroll gardens, brooklyn heights, williamsburg, park slope, fort greene, and clinton hill. lots of young professionals living there, you can find good access to subways in each of those places to get to stern, and they are some fun neighborhoods.
i just know it's a beast when you are first moving here to figure out where to look, so wanted to throw it onto people's radars!