Another benefit of having dogs in New York is that you are surrounded by hundreds of other like-minded folks. Because of this, there are numerous dog parks perfect for any kind of dog. There are even parks for big dogs and small dogs so no one feels too intimidated. New York also has lots of dog-friendly establishments where you can enjoy a cold beverage while your dog has a water dish.
All around the city you can find enclaves just for dogs to run and play with benches for you to sit and enjoy. There are outdoor sculpture parks you can walk through to show your pup (or yourself) some culture. You can walk on paths through old groves of trees and find respite from the hustle of the city while walking on a smooth and paved path. Make sure you plan ahead for any new excursion so you know where to go and what the local dog rules are.
For a totally different experience, head to the South Street Seaport for a walk along the shore with your salty dog. This is an on-leash area, but the neighborhood is very dog-friendly. After walking along the historic waterfront, you can enjoy some food or a libation (while your pup has some water) at one of the many dog-friendly breweries and restaurants. There is nothing better than walking along the water and then sitting on a porch enjoying a treat with your pup.