Madison Square Park. A short walk from the hotel, the park has its own dog run. Jemmy's Dog Run sits near 24th Street, with separate areas for small and large dogs and water on hand. It's named after James Madison, whose nickname was Jemmy. The morning crowd is mostly regulars, and the dogs are usually more social than their owners.
Morning and evening walks. Park Ave So is wide and easy to walk. The side streets of Murray Hill, just east of the hotel, are quieter and lined with brownstones. Most dogs prefer those.
Central Park. Worth the trip if your dog likes space. Under NYC Parks rules, dogs can be off leash in designated areas from 6-9am and from 9pm-1am. Outside those hours, leashes are required.