Absolutely! There are dog runs in many of the parks (Riverside Park, Central Park, just off the top of my head) and most outdoor cafes will cater to the dogs - they bring them cookies, bowls of ice water, etc. Manhattan is a great place for dogs - I envy the pups that live there!
I placed my first pup in NYC last spring. I was a bit worried at first, but they were a young home eager to do their best. It has worked out great! He works from home most the time, when they can't be home during the day they have a dog walker come in and take her out. It is walking distance from a dog park, and they found the best vet they could for her, did their research on the best foods. That is one thing great about placing a dog with folks who can afford to live in the city. They can also afford to give her the best... and she deserves it!
I have placed puppies in NYC and Manhattan over the years with great success. One of my contract conditions was a "dog walker" contract for the families as they both worked outside the home.
Our 6 yr old routinely visits the city when is he assisting his owners with their freelancing jobs in Manhattan for 3-4 months at a time. Living on 7 acres and then moving to concrete is an adjustment for any adult dog. He seems to do fairly well after 1 day of trying to hold in everything. Plenty of dog friendly businesses that provide water and treats outside their shops. He has lived in SOHO, Chelsea, Greenwich and we would take him back in a moment.
We have no problems selling dogs to responsible pet owners in cities, as most have "doggie day care" trips and adventures for the pooches.
We placed one of our pups this year with a family in Manhattan. They already owned a 4 year old Chocolate Boy and were very glad to be bringing in a new friend for him. They lived right across the street from the park, absolutely dog friendly place.